Lian-Ping Wang | Southern University of Science and Technology (original) (raw)

Papers by Lian-Ping Wang

Atmospheric Chemistry and Physics Discussions, 2014

This paper discusses impacts of cloud and precipitation processes on macrophysical properties of ... more This paper discusses impacts of cloud and precipitation processes on macrophysical properties of shallow convective clouds as simulated by a large-eddy model applying warm-rain bin microphysics. Simulations with and without collision-coalescence are considered with CCN concentrations of 30, 60, 120, and 240 mg⁻¹. Simulations with collision-coalescence include either the traditional gravitational collision kernel or a novel kernel that includes enhancements due to the small-scale cloud turbulence. Simulations with droplet collisions were discussed in Wyszogrodzki et al. (2013) focusing on the impact of the turbulent collision kernel. The current paper expands that analysis and puts model results in the context of previous studies. Despite a significant increase of the drizzle/rain with the decrease of CCN concentration, enhanced by the impact of the small-scale turbulence, impacts on the macroscopic cloud field characteristics are relatively minor. We doc...

Physical Review E

In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressib... more In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressible gas flows based on the total energy kinetic model [Guo et al., Phys. Rev. E 75, 036704 (2007)]. The proposed DUGKS can be viewed as a special finite-volume lattice Boltzmann method for the compressible Navier-Stokes equations in the double distribution function formulation, in which the mass and momentum transport are described by the kinetic equation for a density distribution function (g), and the energy transport is described by the other one for an energy distribution function (h). To recover the full compressible Navier-Stokes equations exactly, the corresponding equilibrium distribution functions g eq and h eq are expanded as Hermite polynomials up to third and second orders, respectively. The velocity spaces for the kinetic equations are discretized according to the seventh and fifth Gauss-Hermite quadratures. Consequently, the computational efficiency of the present DUGKS can be much improved in comparison with previous versions using more discrete velocities required by the ninth Gauss-Hermite quadrature.

Physical Review E

In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across ... more In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.

HAL (Le Centre pour la Communication Scientifique Directe), May 19, 2019

A direct numerical simulation (DNS) code is developed to simulate immiscible two-phase flows base... more A direct numerical simulation (DNS) code is developed to simulate immiscible two-phase flows based on the recently developed discrete unified gas-kinetic scheme (DUGKS). This scheme simulates hydrodynamic equations of the quasi-incompressible Cahn-Hilliard-Navier-Stokes system by the use of two mesoscopic distributions and the proper design of their equilibrium distributions and source terms. Several immiscible two-phase flows are used to validate the scheme in both 2D and 3D, including a stationary droplet in 2D and 3D, the Rayleigh-Taylor flows, and two-phase homogeneous isotropic decaying turbulence. The results obtained by DUGKS are compared carefully to these from the literature and the ARCHER code, i.e., a Coupled Level Set-Volume of Fluid (CLSVOF) method. The comparisons indicate that DUGKS is a promising scheme for direct numerical simulations of immiscible two-phase flows.

In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning m... more In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning moving rigid solid particles suspended a viscous fluid. Three aspects relevant to the interaction between flow of a viscous fluid and moving solid boundaries are considered. First, the popular interpolated bounce back scheme is examined both theoretically and numerically. It is important to recognize that even though significant efforts had previously been devoted to the performance, especially the accuracy, of different interpolated bounce back schemes for a fixed boundary, there were relatively few studies focusing on moving solid surfaces. In this study, different interpolated bounce back schemes are compared theoretically for a moving boundary. Then, several benchmark cases are presented to show their actual performance in numerical simulations. Second, we examine different implementations of the momentum exchange method to calculate hydrodynamic force and torque acting on a moving surface. The momentum exchange method is well established for fixed solid boundaries, however, for moving solid boundaries there are still open issues such as unphysical force fluctuations and Galilean invariance errors. Recent progress in this direction is discussed, along with our own interpretations and modifications. Several benchmark cases, including a particle-laden turbulent channel flow, are used to demonstrate the effects of different modifications on the accuracy and physical results under different physical configurations. The third aspect is the refilling scheme for constructing the unknown distribution functions for the new fluid nodes that emerge from the previous solid region as a particle moves relative to a fixed lattice grid. We examine and compare the performance of the refilling schemes introduced by Lallemand & Luo (2003), Li et al.(2004), and Caiazzo (2008). We demonstrate that improvements can be made to suppress force fluctuations resulting from refilling.

Physics of Fluids

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a... more In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well wi...

In this paper, we present a general framework for the inverse-design of mesoscopic models based o... more In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the t...

Journal of Computational Physics: X, 2021

Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for s... more Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for simulating flows at all Knudsen numbers. In this study, we extend DUGKS to simulate fully compressible thermal flows. We introduce a source term to the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) collision model [1] to adjust heat flux and thus the Prandtl number. The fully compressible Navier-Stokes equations can be recovered by the current model. As a mesoscopic CFD approach, it requires an accurate mesoscopic implementation of the boundary conditions. Using the Chapman-Enskog approximation, we derive the "bounce-back" expressions for both temperature and velocity distribution functions, which reveal the need to consider coupling terms between the velocity and thermal fields. To validate our scheme, we first reproduce the Boussinesq flow results by simulating natural convection in a square cavity with a small temperature difference (= 0.01) and a low Mach number. Then we perform simulations of steady natural convection (Ra = 1.0 × 10 6) in a square cavity with differentially heated side walls and a large temperature difference (= 0.6), where the Boussinesq approximation becomes invalid. Temperature, velocity profiles, and Nusselt number distribution are obtained and compared with the benchmark results from the literature. Finally, the unsteady compressible natural convection with Ra = 5.0 × 10 9 , = 0.6 is studied and the turbulent fluctuation statistics are computed and analyzed.

Physics of Fluids

Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann metho... more Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann method (LBM) when reproducing the no-slip condition at a solid boundary. While the lattice Boltzmann equation used in LBM for interior nodes is known to reproduce the Navier-Stokes (N-S) equations under the Chapman-Enskog (CE) approximation, the unknown distribution functions reconstructed from a bounce-back scheme at boundary nodes may not be consistent with the CE approximation. This problem could lead to undesirable effects such as non-physical slip velocity, grid-scale velocity and pressure noises, the local inconsistency with the N-S equations, and sometimes even a reduction of the overall numerical-accuracy order of LBM. Here we provide a systematic study of these undesirable effects. We first derive the explicit structure of the mesoscopic distribution function for interior nodes. Then the bounce-back distribution function is examined to identify the hidden errors. It is shown that the...

doi:10.1088/1367-2630/10/7/075013 Abstract. The collision efficiency of sedimenting cloud droplet... more doi:10.1088/1367-2630/10/7/075013 Abstract. The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision–coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51–73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20µm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100 cm2 s−3, respectively. The collision...

Lecture Notes in Computer Science, 2012

This paper presents a comprehensive story of the development of simpler performance models for di... more This paper presents a comprehensive story of the development of simpler performance models for distributed implementations of the Fast Fourier Transform in 3 Dimensions (FFT3D). We start by providing an overview of several implementations and their performance models. Then, we present arguments to support the use of a simple power function instead of the full performance models proposed by other publications. We argue that our model can be obtained for a particular problem size with minimal experimentation while other models require significant tuning to determine their constants. Our advocacy for simpler performance models is inspired by the difficulties found when estimating the performance of FFT3D programs. Correctly estimating how well large-scale programs (such as FFT3D) will work is one of the most challenging problems faced by scientists. The significant effort devoted to this problem has resulted in the appearance of numerous works on performance modeling. The results produced by an exhaustive performance modeling study may predict the performance of a program with a reasonably good accuracy. However, those studies may become unusable because their aim for accuracy can make them so difficult and cumbersome to use that direct experimentation with the program may be preferable, defeating their original purpose. We propose an alternative approach in this paper that does not require a full, accurate, performance model. Our approach mitigates the problem of existing performance models, each one of the parameters and constants in the model has to be carefully measured and tuned, a process that is intrinsically harder than direct experimentation with the program at hand. Instead, we were able to simplify our approach by (1) building performance models that target particular applications in their normal operating conditions and (2) using simpler models that still produce good approximations for the particular case of a program's normal operating environment. We have conducted experiments using the Blue Fire Supercomputer at the National Center for Atmospheric Research (NCAR), showing that our simplified model can predict the performance of a particular implementation with a high degree of accuracy and very little effort when the program is used in its intended operating range. Demystifying Performance Predictions of Distributed FFT3D Implementations 197 Finally, although our performance model does not cover extreme cases, we show that its simple approximation under the normal operating conditions of FFT3D is able to provide solid, useful approximations.

New Journal of Physics, 2008

The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input par... more The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision-coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51-73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20 µm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100 cm 2 s −3 , respectively. The collision efficiency for self-collisions in a bidisperse turbulent suspension can be larger than one. Such an increase in self-collisions is related to the farfield many-body AI and depends on the volumetric concentration of droplets. The total turbulent enhancement agrees qualitatively with previous results, but differs on a quantitative level. In the case of cross-size collisions between 18 and 20 µm droplets, the total turbulent enhancement can be a factor of 7 and 2 at 3 Author to whom any correspondence should be addressed.

New Journal of Physics, 2008

The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted... more The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted if the effects of air turbulence on two kinematic pair statistics can be modeled. The first is the average radial relative velocity and the second is the radial distribution function (RDF). A survey of the literature shows that no theory is available for predicting the radial relative velocity of finite-inertia sedimenting droplets in a turbulent flow. In this paper, a theory for the radial relative velocity is developed, using a statistical approach assuming that gravitational sedimentation dominates the relative motion of droplets before collision. In the weak-inertia limit, the theory reveals a new term making a positive contribution to the radial relative velocity resulting from a coupling between sedimentation and air turbulence on the motion of finite-inertia droplets. The theory is compared to the direct numerical simulations (DNS) results in part 1, showing a reasonable agreement with the DNS data for bidisperse cloud droplets. For droplets larger than 30 µm in radius, a nonlinear drag (NLD) can also be included in the theory in terms of an effective inertial response time and an effective terminal velocity. In addition, an empirical model is developed to quantify the RDF. This, together with the theory for radial relative velocity, provides a parameterization for the turbulent geometric collision kernel. Using this integrated model, we find that turbulence could triple the geometric collision kernel, relative to the stagnant air case, for a droplet pair of 10 and 20 µm sedimenting through a cumulus cloud at R λ = 2 × 10 4 and = 600 cm 2 s −3 .

Nanoscale, 2013

A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon ... more A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon nanotube (CNT) continuous fibers under twisting and tension is conducted using coarse-grained molecular dynamics simulations. The tensile strength of CNT fibers with random CNT stacking is found to be higher than that of fibers with regular CNT stacking. The factor dominating the mechanical response of CNT fibers is identified as individual CNT stretching. A simplified twisted CNT fiber model is studied to illustrate the structural evolution mechanisms of CNT fibers under tension. Moreover, it is demonstrated that CNT fibers can be reinforced by enhancing intertube interactions. This study would be helpful not only in the general understanding of the nano-and micro-scale factors affecting CNT fibers' mechanical behavior, but also in the optimal design of CNT fibers' architecture and performance.

Journal of Physics: Conference Series, 2011

The development of precipitating warm clouds is affected by several effects of small-scale air tu... more The development of precipitating warm clouds is affected by several effects of small-scale air turbulence including enhancement of droplet-droplet collision rate by turbulence, entrainment and mixing at the cloud edges, and coupling of mechanical and thermal energies at various scales. Large-scale computation is a viable research tool for quantifying these multiscale processes. Specifically, top-down large-eddy simulations (LES) of shallow convective clouds typically resolve scales of turbulent energy-containing eddies while the effects of turbulent cascade toward viscous dissipation are parameterized. Bottom-up hybrid direct numerical simulations (HDNS) of cloud microphysical processes resolve fully the dissipation-range flow scales but only partially the inertial subrange scales. it is desirable to systematically decrease the grid length in LES and increase the domain size in HDNS so that they can be better integrated to address the full range of scales and their coupling. In this paper, we discuss computational issues and physical modeling questions in expanding the ranges of scales realizable in LES and HDNS, and in bridging LES and HDNS. We review our ongoing efforts in transforming our simulation codes towards PetaScale computing, in improving physical representations in LES and HDNS, and in developing better methods to analyze and interpret the simulation results.

Acta Mechanica

Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Gmb... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag GmbH Austria, part of Springer Nature. This eoffprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Direct numerical simulation of three-dimensional (3D) viscous flow in a wavy pipe is performed us... more Direct numerical simulation of three-dimensional (3D) viscous flow in a wavy pipe is performed using the lattice Boltzmann approach, to study 3D flow features in a curved pipe with nonuniform curvature. We first validate the lattice Boltzmann approach by simulating a transient flow in a straight pipe. In a wavy pipe, it is shown that the pressure gradient necessary to drive the flow depends more strongly on the flow Reynolds number, due to curvature-induced fluid inertial force and transverse secondary flows. The wavy pipe could provide a simple design for enhancing mixing and heat transfer in pipes.

Kinematic descriptions of the rate of collision between two groups of particles are central to a ... more Kinematic descriptions of the rate of collision between two groups of particles are central to a variety of problems in cloud microphysics, engineering applications, and statistical mechanics. When particles are uniformly distributed, the collision kernel ⌫ depends on the statistics of relative velocities among colliding particles. In the pioneering work by Saffman and Turner ͓"On the collision of drops in turbulent clouds," J. Fluid Mech. 1, 16 ͑1956͔͒, two different formulations were used to calculate ⌫ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial or longitudinal component w r of the relative velocity w between two particles at contact: ⌫ sph =2R 2 ͉͗w r ͉͘, where R is the geometric collision radius. The second or cylindrical formulation is based on the vector velocity itself: ⌫ cyl = R 2 ͉͗w͉͘. It was shown previously by Wang et al. ͓"Statical mechanical descriptions of turbulent coagulati...

Physics of Fluids

Chunhua Zhang (张春华), Zhaoli Guo (郭照立) and Lian-Ping Wang (王连平) COLLECTIONS Paper published as par... more Chunhua Zhang (张春华), Zhaoli Guo (郭照立) and Lian-Ping Wang (王连平) COLLECTIONS Paper published as part of the special topic on Special Issue on the Lattice Boltzmann Method

Atmospheric Chemistry and Physics Discussions, 2014

This paper discusses impacts of cloud and precipitation processes on macrophysical properties of ... more This paper discusses impacts of cloud and precipitation processes on macrophysical properties of shallow convective clouds as simulated by a large-eddy model applying warm-rain bin microphysics. Simulations with and without collision-coalescence are considered with CCN concentrations of 30, 60, 120, and 240 mg⁻¹. Simulations with collision-coalescence include either the traditional gravitational collision kernel or a novel kernel that includes enhancements due to the small-scale cloud turbulence. Simulations with droplet collisions were discussed in Wyszogrodzki et al. (2013) focusing on the impact of the turbulent collision kernel. The current paper expands that analysis and puts model results in the context of previous studies. Despite a significant increase of the drizzle/rain with the decrease of CCN concentration, enhanced by the impact of the small-scale turbulence, impacts on the macroscopic cloud field characteristics are relatively minor. We doc...

Physical Review E

In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressib... more In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressible gas flows based on the total energy kinetic model [Guo et al., Phys. Rev. E 75, 036704 (2007)]. The proposed DUGKS can be viewed as a special finite-volume lattice Boltzmann method for the compressible Navier-Stokes equations in the double distribution function formulation, in which the mass and momentum transport are described by the kinetic equation for a density distribution function (g), and the energy transport is described by the other one for an energy distribution function (h). To recover the full compressible Navier-Stokes equations exactly, the corresponding equilibrium distribution functions g eq and h eq are expanded as Hermite polynomials up to third and second orders, respectively. The velocity spaces for the kinetic equations are discretized according to the seventh and fifth Gauss-Hermite quadratures. Consequently, the computational efficiency of the present DUGKS can be much improved in comparison with previous versions using more discrete velocities required by the ninth Gauss-Hermite quadrature.

Physical Review E

In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across ... more In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.

HAL (Le Centre pour la Communication Scientifique Directe), May 19, 2019

A direct numerical simulation (DNS) code is developed to simulate immiscible two-phase flows base... more A direct numerical simulation (DNS) code is developed to simulate immiscible two-phase flows based on the recently developed discrete unified gas-kinetic scheme (DUGKS). This scheme simulates hydrodynamic equations of the quasi-incompressible Cahn-Hilliard-Navier-Stokes system by the use of two mesoscopic distributions and the proper design of their equilibrium distributions and source terms. Several immiscible two-phase flows are used to validate the scheme in both 2D and 3D, including a stationary droplet in 2D and 3D, the Rayleigh-Taylor flows, and two-phase homogeneous isotropic decaying turbulence. The results obtained by DUGKS are compared carefully to these from the literature and the ARCHER code, i.e., a Coupled Level Set-Volume of Fluid (CLSVOF) method. The comparisons indicate that DUGKS is a promising scheme for direct numerical simulations of immiscible two-phase flows.

In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning m... more In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning moving rigid solid particles suspended a viscous fluid. Three aspects relevant to the interaction between flow of a viscous fluid and moving solid boundaries are considered. First, the popular interpolated bounce back scheme is examined both theoretically and numerically. It is important to recognize that even though significant efforts had previously been devoted to the performance, especially the accuracy, of different interpolated bounce back schemes for a fixed boundary, there were relatively few studies focusing on moving solid surfaces. In this study, different interpolated bounce back schemes are compared theoretically for a moving boundary. Then, several benchmark cases are presented to show their actual performance in numerical simulations. Second, we examine different implementations of the momentum exchange method to calculate hydrodynamic force and torque acting on a moving surface. The momentum exchange method is well established for fixed solid boundaries, however, for moving solid boundaries there are still open issues such as unphysical force fluctuations and Galilean invariance errors. Recent progress in this direction is discussed, along with our own interpretations and modifications. Several benchmark cases, including a particle-laden turbulent channel flow, are used to demonstrate the effects of different modifications on the accuracy and physical results under different physical configurations. The third aspect is the refilling scheme for constructing the unknown distribution functions for the new fluid nodes that emerge from the previous solid region as a particle moves relative to a fixed lattice grid. We examine and compare the performance of the refilling schemes introduced by Lallemand & Luo (2003), Li et al.(2004), and Caiazzo (2008). We demonstrate that improvements can be made to suppress force fluctuations resulting from refilling.

Physics of Fluids

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a... more In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well wi...

In this paper, we present a general framework for the inverse-design of mesoscopic models based o... more In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the t...

Journal of Computational Physics: X, 2021

Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for s... more Discrete unified gas-kinetic scheme (DUGKS) has been developed recently as a general method for simulating flows at all Knudsen numbers. In this study, we extend DUGKS to simulate fully compressible thermal flows. We introduce a source term to the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) collision model [1] to adjust heat flux and thus the Prandtl number. The fully compressible Navier-Stokes equations can be recovered by the current model. As a mesoscopic CFD approach, it requires an accurate mesoscopic implementation of the boundary conditions. Using the Chapman-Enskog approximation, we derive the "bounce-back" expressions for both temperature and velocity distribution functions, which reveal the need to consider coupling terms between the velocity and thermal fields. To validate our scheme, we first reproduce the Boussinesq flow results by simulating natural convection in a square cavity with a small temperature difference (= 0.01) and a low Mach number. Then we perform simulations of steady natural convection (Ra = 1.0 × 10 6) in a square cavity with differentially heated side walls and a large temperature difference (= 0.6), where the Boussinesq approximation becomes invalid. Temperature, velocity profiles, and Nusselt number distribution are obtained and compared with the benchmark results from the literature. Finally, the unsteady compressible natural convection with Ra = 5.0 × 10 9 , = 0.6 is studied and the turbulent fluctuation statistics are computed and analyzed.

Physics of Fluids

Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann metho... more Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann method (LBM) when reproducing the no-slip condition at a solid boundary. While the lattice Boltzmann equation used in LBM for interior nodes is known to reproduce the Navier-Stokes (N-S) equations under the Chapman-Enskog (CE) approximation, the unknown distribution functions reconstructed from a bounce-back scheme at boundary nodes may not be consistent with the CE approximation. This problem could lead to undesirable effects such as non-physical slip velocity, grid-scale velocity and pressure noises, the local inconsistency with the N-S equations, and sometimes even a reduction of the overall numerical-accuracy order of LBM. Here we provide a systematic study of these undesirable effects. We first derive the explicit structure of the mesoscopic distribution function for interior nodes. Then the bounce-back distribution function is examined to identify the hidden errors. It is shown that the...

doi:10.1088/1367-2630/10/7/075013 Abstract. The collision efficiency of sedimenting cloud droplet... more doi:10.1088/1367-2630/10/7/075013 Abstract. The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision–coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51–73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20µm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100 cm2 s−3, respectively. The collision...

Lecture Notes in Computer Science, 2012

This paper presents a comprehensive story of the development of simpler performance models for di... more This paper presents a comprehensive story of the development of simpler performance models for distributed implementations of the Fast Fourier Transform in 3 Dimensions (FFT3D). We start by providing an overview of several implementations and their performance models. Then, we present arguments to support the use of a simple power function instead of the full performance models proposed by other publications. We argue that our model can be obtained for a particular problem size with minimal experimentation while other models require significant tuning to determine their constants. Our advocacy for simpler performance models is inspired by the difficulties found when estimating the performance of FFT3D programs. Correctly estimating how well large-scale programs (such as FFT3D) will work is one of the most challenging problems faced by scientists. The significant effort devoted to this problem has resulted in the appearance of numerous works on performance modeling. The results produced by an exhaustive performance modeling study may predict the performance of a program with a reasonably good accuracy. However, those studies may become unusable because their aim for accuracy can make them so difficult and cumbersome to use that direct experimentation with the program may be preferable, defeating their original purpose. We propose an alternative approach in this paper that does not require a full, accurate, performance model. Our approach mitigates the problem of existing performance models, each one of the parameters and constants in the model has to be carefully measured and tuned, a process that is intrinsically harder than direct experimentation with the program at hand. Instead, we were able to simplify our approach by (1) building performance models that target particular applications in their normal operating conditions and (2) using simpler models that still produce good approximations for the particular case of a program's normal operating environment. We have conducted experiments using the Blue Fire Supercomputer at the National Center for Atmospheric Research (NCAR), showing that our simplified model can predict the performance of a particular implementation with a high degree of accuracy and very little effort when the program is used in its intended operating range. Demystifying Performance Predictions of Distributed FFT3D Implementations 197 Finally, although our performance model does not cover extreme cases, we show that its simple approximation under the normal operating conditions of FFT3D is able to provide solid, useful approximations.

New Journal of Physics, 2008

The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input par... more The collision efficiency of sedimenting cloud droplets in a turbulent air flow is a key input parameter in predicting the growth of cloud droplets by collision-coalescence. In this study, turbulent collision efficiency was directly computed, using a hybrid direct numerical simulation (HDNS) approach (Ayala et al 2007 J. Comput. Phys. 225 51-73). The HDNS results show that air turbulence enhances the collision efficiency partly due to the fact that aerodynamic interactions (AIs) become less effective in reducing the relative motion of droplets in the presence of background air turbulence. The level of increase in the collision efficiency depends on the flow dissipation rate and the droplet size ratio. For example, the collision efficiency between droplets of 18 and 20 µm in radii is increased by air turbulence (relative to the stagnant air case) by a factor of 4 and 1.6 at dissipation rates of 400 and 100 cm 2 s −3 , respectively. The collision efficiency for self-collisions in a bidisperse turbulent suspension can be larger than one. Such an increase in self-collisions is related to the farfield many-body AI and depends on the volumetric concentration of droplets. The total turbulent enhancement agrees qualitatively with previous results, but differs on a quantitative level. In the case of cross-size collisions between 18 and 20 µm droplets, the total turbulent enhancement can be a factor of 7 and 2 at 3 Author to whom any correspondence should be addressed.

New Journal of Physics, 2008

The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted... more The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted if the effects of air turbulence on two kinematic pair statistics can be modeled. The first is the average radial relative velocity and the second is the radial distribution function (RDF). A survey of the literature shows that no theory is available for predicting the radial relative velocity of finite-inertia sedimenting droplets in a turbulent flow. In this paper, a theory for the radial relative velocity is developed, using a statistical approach assuming that gravitational sedimentation dominates the relative motion of droplets before collision. In the weak-inertia limit, the theory reveals a new term making a positive contribution to the radial relative velocity resulting from a coupling between sedimentation and air turbulence on the motion of finite-inertia droplets. The theory is compared to the direct numerical simulations (DNS) results in part 1, showing a reasonable agreement with the DNS data for bidisperse cloud droplets. For droplets larger than 30 µm in radius, a nonlinear drag (NLD) can also be included in the theory in terms of an effective inertial response time and an effective terminal velocity. In addition, an empirical model is developed to quantify the RDF. This, together with the theory for radial relative velocity, provides a parameterization for the turbulent geometric collision kernel. Using this integrated model, we find that turbulence could triple the geometric collision kernel, relative to the stagnant air case, for a droplet pair of 10 and 20 µm sedimenting through a cumulus cloud at R λ = 2 × 10 4 and = 600 cm 2 s −3 .

Nanoscale, 2013

A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon ... more A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon nanotube (CNT) continuous fibers under twisting and tension is conducted using coarse-grained molecular dynamics simulations. The tensile strength of CNT fibers with random CNT stacking is found to be higher than that of fibers with regular CNT stacking. The factor dominating the mechanical response of CNT fibers is identified as individual CNT stretching. A simplified twisted CNT fiber model is studied to illustrate the structural evolution mechanisms of CNT fibers under tension. Moreover, it is demonstrated that CNT fibers can be reinforced by enhancing intertube interactions. This study would be helpful not only in the general understanding of the nano-and micro-scale factors affecting CNT fibers' mechanical behavior, but also in the optimal design of CNT fibers' architecture and performance.

Journal of Physics: Conference Series, 2011

The development of precipitating warm clouds is affected by several effects of small-scale air tu... more The development of precipitating warm clouds is affected by several effects of small-scale air turbulence including enhancement of droplet-droplet collision rate by turbulence, entrainment and mixing at the cloud edges, and coupling of mechanical and thermal energies at various scales. Large-scale computation is a viable research tool for quantifying these multiscale processes. Specifically, top-down large-eddy simulations (LES) of shallow convective clouds typically resolve scales of turbulent energy-containing eddies while the effects of turbulent cascade toward viscous dissipation are parameterized. Bottom-up hybrid direct numerical simulations (HDNS) of cloud microphysical processes resolve fully the dissipation-range flow scales but only partially the inertial subrange scales. it is desirable to systematically decrease the grid length in LES and increase the domain size in HDNS so that they can be better integrated to address the full range of scales and their coupling. In this paper, we discuss computational issues and physical modeling questions in expanding the ranges of scales realizable in LES and HDNS, and in bridging LES and HDNS. We review our ongoing efforts in transforming our simulation codes towards PetaScale computing, in improving physical representations in LES and HDNS, and in developing better methods to analyze and interpret the simulation results.

Acta Mechanica

Your article is protected by copyright and all rights are held exclusively by Springer-Verlag Gmb... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag GmbH Austria, part of Springer Nature. This eoffprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Direct numerical simulation of three-dimensional (3D) viscous flow in a wavy pipe is performed us... more Direct numerical simulation of three-dimensional (3D) viscous flow in a wavy pipe is performed using the lattice Boltzmann approach, to study 3D flow features in a curved pipe with nonuniform curvature. We first validate the lattice Boltzmann approach by simulating a transient flow in a straight pipe. In a wavy pipe, it is shown that the pressure gradient necessary to drive the flow depends more strongly on the flow Reynolds number, due to curvature-induced fluid inertial force and transverse secondary flows. The wavy pipe could provide a simple design for enhancing mixing and heat transfer in pipes.

Kinematic descriptions of the rate of collision between two groups of particles are central to a ... more Kinematic descriptions of the rate of collision between two groups of particles are central to a variety of problems in cloud microphysics, engineering applications, and statistical mechanics. When particles are uniformly distributed, the collision kernel ⌫ depends on the statistics of relative velocities among colliding particles. In the pioneering work by Saffman and Turner ͓"On the collision of drops in turbulent clouds," J. Fluid Mech. 1, 16 ͑1956͔͒, two different formulations were used to calculate ⌫ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial or longitudinal component w r of the relative velocity w between two particles at contact: ⌫ sph =2R 2 ͉͗w r ͉͘, where R is the geometric collision radius. The second or cylindrical formulation is based on the vector velocity itself: ⌫ cyl = R 2 ͉͗w͉͘. It was shown previously by Wang et al. ͓"Statical mechanical descriptions of turbulent coagulati...

Physics of Fluids

Chunhua Zhang (张春华), Zhaoli Guo (郭照立) and Lian-Ping Wang (王连平) COLLECTIONS Paper published as par... more Chunhua Zhang (张春华), Zhaoli Guo (郭照立) and Lian-Ping Wang (王连平) COLLECTIONS Paper published as part of the special topic on Special Issue on the Lattice Boltzmann Method