A non-iterative immersed boundary method for spherical particles of arbitrary density ratio (original) (raw)
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A general implicit direct forcing immersed boundary method for rigid particles
Computers & Fluids, 2018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Generalized non-iterative IBM for arbitrary rigid particles. • Unconditional numerical stability for arbitrary fluid-particle interactions. • Easy switching from weakly coupled direct forcing IBM to strong coupling. • Simulation of various test cases, commonly unstable using weak coupling schemes.
An improved immersed boundary method with direct forcing for the simulation of particle laden flows
Journal of Computational Physics, 2012
An efficient approach for the simulation of finite-size particles with interface resolution was presented by Uhlmann [M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys. 209 (2005) 448-476.]. The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling yielding a substantially better imposition of boundary conditions at the interface, even for large time steps. Furthermore, it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1, hence excluding, for example, non-buoyant particles. This can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0.3. This paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size. A remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner. The resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method.
A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communications between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids are improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the non-slip and non-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computing cost remains much lower than them and nearly equivalent to the conventional DF method. The dependence of the optimum thickness value of boundary thickening on the form of the different regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re = 0.1), steady vortex separating flow (Re = 40) and unsteady vortex shedding flow (Re = 200) around a circular cylinder. The accuracy and robustness of the present method for moving particle-laden flows are performed on three benchmark cases, such as free sedimentation of single circular cylinder, DKT sedimentation of two particles and Rayleigh-Taylor instability of 504 particles sedimentation in an enclosed cavity. The computational efficiency between the present BTDF method and the MDF method is also compared at last.
Numerical simulation of particle motion using a combined MacCormack and immersed boundary method
A numerical approach is presented for the direct numerical simulation of particle motion that combines the MacCormack scheme and the immersed boundary method. It exhibits the advantageous features of the explicit MacCormack scheme which is second-order accurate in time and space with simplicity in programing. The approach solves the compressible Navier–Stokes equations and uses the immersed boundary method to tackle the interactions between the fluid and the suspended particles. The force due to the interaction of two phases is computed via an elastic forcing method. The numerical approach is validated using uniform flow past a stationary circular cylinder, sedimentation of circular discs, and particle motion (orientation and translation) in unidirectional flows. Results are also compared to simulation obtained from a mixture model for solid particles for the same flow conditions.
Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids
Journal of Fluid Mechanics, 2012
The paper presents a model for particle–particle and particle–wall collisions during interface-resolving numerical simulations of particle-laden flows. The accurate modelling of collisions in this framework is challenging due to methodological problems generated by interface approach and contact as well as due to the greatly different time scales involved. To cope with this situation, multiscale modelling approaches are introduced avoiding excessive local grid refinement during surface approach and time step reduction during the surface contact. A new adaptive model for the normal forces in the phase of ‘dry contact’ is proposed, stretching the collision process in time to match the time step of the fluid solver. This yields a physically sound and robust collision model with modified stiffness and damping determined by an optimization scheme. Furthermore, the model is supplemented with a new approach for modelling the tangential force during oblique collisions which is based on two ...
Fluid dynamics of floating particles
Journal of Fluid Mechanics, 2005
We have developed a numerical package to simulate particle motions in fluid interfaces. The particles are moved in a direct simulation respecting the fundamental equations of motion of fluids and solid particles without the use of models. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the interface is moved by the method of level sets. The present work fills a gap since there are no other theoretical methods available to describe the nonlinear fluid dynamics of capillary attraction.
Volume 1: Symposia, Parts A and B, 2005
In an attempt to develop a reliable numerical method that can deal economically with a large number of rigid particles moving in an incompressible Newtonian fluid at a reasonable cost, we consider two fictitious-domain methods: a Constant-density Explicit Volumetric forcing method (CEV) and a Variable-density Implicit Volumetric forcing method (VIV). In both methods, the mutual interaction between the solid and the fluid phase is taken into account by an additional body force term to the Navier-Stokes equations, but the physical meaning of the forcing is different for the two methods. In the CEV method, which is built on a constantdensity Navier-Stokes solver, the net forcing added to the fluid is generally not zero, and must be cancelled by applying Newton's first law to a rigid particle template which has the same shape as the rigid particle and carries the "excess mass" of the rigid particle, i.e. the excess over the mass of the displaced fluid. The "target velocity" to which one forces the velocity within the particle is evaluated through the equation of motion for the rigid particle template. In the VIV method, built on a variable-density incompressible flow solver, the rigid particle (angular) velocity is determined by averaging the (angular) momentum, within the particle domain, of the fractional-step velocity field, and the net forcing is zero. By design, this method does not require any rigid particle template equations, so it can be applied for both neutral and non-neutral density ratios without any difficulties. We consider two test problems with single freely moving circular disks: a disk falling in quiescent fluid, and a disk in Poiseuille channel flow. At near-neutral density ratios, the CEV method is found to perform better, while the VIV method yields more accurate results at higher relative density ratios.
Inertial coupling method for particles in an incompressible fluctuating fluid
Computer Methods in Applied Mechanics and Engineering, 2014
We develop an inertial coupling method for modeling the dynamics of point-like "blob" particles immersed in an incompressible fluid, generalizing previous work for compressible fluids [F. Balboa Usabiaga, I. Pagonabarraga, and R. Delgado-Buscalioni, J. Comp. Phys., 235:701-722, 2013 ]. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels allow the blob to provide an effective model of a particle; specifically, the volume, mass, and hydrodynamic properties of the blob are remarkably grid-independent. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems. In the deterministic setting, we find the blob to be a remarkably robust approximation to a rigid sphere, at both low and high Reynolds numbers. In the stochastic setting, we study in detail the short and long-time behavior of the velocity autocorrelation function and observe agreement with all of the known behavior for rigid sphere immersed in a fluctuating fluid. The proposed inertial coupling method provides a low-cost coarse-grained (minimal resolution) model of particulate flows over a wide range of time-scales ranging from Brownian to convection-driven motion. -resolved particulate flows for example, semi-implicit CFD schemes. Moreover, they cannot be adapted to efficiently treat the natural time scales governing the different dynamical regimes (e.g., the Brownian or overdamped limit). Similar advantages and drawbacks also apply to the lattice Boltzmann (LB) method [3], although the LB approach has proven to be a rather flexible framework .
A spherical kernel for the Finite Volume Particle Method and application to surface tension
2016
We have recently developed a conservative finite volume particle method (FVPM) that can efficiently model 2D and 3D fluid flow with free-surfaces and complex geometry, as well as fluid-structure interaction. In this paper we present a new FVPM formulation that features spherical kernel support in place of the original cubic support. Spherical kernels have no directionality and result in smooth interactions between particles, which improves the accuracy and robustness of the method. Building on the spherical kernel FVPM, we introduce a new surface tension model. The formulation, derived from a physical model, is based on macroscopic symmetrical particle-particle interaction forces and results in a stable surface tension force with no ad-hoc parameters.
Smooth particle approach for surface tension calculation in moving particle semi-implicit method
We present here an algorithm to solve three-dimensional multi-phase flow problems based on the moving particle semi-implicit (MPS) method. The method is fully Lagrangian and can treat flows with large deformations of the interface such as encountered in the break-up and coalescence of drops. The mean curvature and normal vector of the interface, needed for surface tension calculation, are estimated by a blending of smooth particle hydrodynamics (SPH) and MPS differential schemes. The method is applied to two problems: the free oscillation of a droplet and the transition of a falling drop into a vortex ring. The results are consistent with theory and experiment. This method can be successfully applied to the calculation of a process in planetary core formation, where centimetre scale liquid metal droplets form an emulsion in liquid silicate.