Kelvin-Helmholtz instabilities in smoothed particle hydrodynamics (original) (raw)

Kelvin-Helmholtz instabilities with Godunov smoothed particle hydrodynamics

Monthly Notices of the Royal Astronomical Society, 2010

Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka. The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high-density contrast, while the standard SPH shows the absence of the instability across a density gradient. The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instabilities. The blob test result coincides well with the results of the grid-based codes.

Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics

Monthly Notices of the Royal Astronomical Society, 2011

We present results based on an implementation of the Godunov smoothed particle hydrodynamics (GSPH), originally developed by Inutsuka, in the GADGET-3 hydrodynamic code. We first review the derivation of the GSPH discretization of the equations of moment and energy conservation, starting from the convolution of these equations with the interpolating kernel. The two most important aspects of the numerical implementation of these equations are (a) the appearance of fluid velocity and pressure obtained from the solution of the Riemann problem between each pair of particles, and (b) the absence of an artificial viscosity term. We carry out three different controlled hydrodynamical three-dimensional tests, namely the Sod shock tube, the development of Kelvin-Helmholtz instabilities in a shear-flow test and the 'blob' test describing the evolution of a cold cloud moving against a hot wind.

Numerical modeling of Kelvin–Helmholtz instability using smoothed particle hydrodynamics

problem of an incompressible two-phase immiscible fluid in a stratified inviscid shear flow with interfacial tension. The time-dependent evolution of the two-fluid interface over a wide range of Richardson number (Ri) and for three different density ratios is numerically investigated. The simulation results are compared with analytical solutions in the linear regime. Having captured the physics behind KHI, the effects of gravity and surface tension on a two-dimensional shear layer are examined independently and together. It is shown that the growth rate of the KHI is mainly controlled by the value of the Ri number, not by the nature of the stabilizing forces. It was observed that the SPH method requires a Richardson number lower than unity (i.e. Ri ∼ = 0.8) for the onset of KHI, and that the artificial viscosity plays a significant role in obtaining physically correct simulation results that are in agreement with analytical solutions. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density ratios. NUMERICAL MODELING OF KELVIN-HELMHOLTZ INSTABILITY USING SPH Figure 7. Time evolution of the interface in the two-dimensional KHI problem for the density ratio of 2 / 1 = 10 at various Ri numbers: (a) t * = 0.5; (b) t * = 1.0; (c) t * = 1.5; and (d) t * = 2.0 ( = 0.001).

Modelling shear flows with smoothed particle hydrodynamics and grid-based methods

Monthly Notices of the Royal Astronomical Society, 2010

Given the importance of shear flows for astrophysical gas dynamics, we study the evolution of the Kelvin-Helmholtz instability (KHI) analytically and numerically. We derive the dispersion relation for the two-dimensional KHI including viscous dissipation. The resulting expression for the growth rate is then used to estimate the intrinsic viscosity of four numerical schemes depending on code-specific as well as on physical parameters. Our set of numerical schemes includes the Tree-SPH code VINE, an alternative smoothed particle hydrodynamics (SPH) formulation developed by Price and the finite-volume grid codes FLASH and PLUTO. In the first part, we explicitly demonstrate the effect of dissipation-inhibiting mechanisms such as the Balsara viscosity on the evolution of the KHI. With VINE, increasing density contrasts lead to a continuously increasing suppression of the KHI (with complete suppression from a contrast of 6:1 or higher). The alternative SPH formulation including an artificial thermal conductivity reproduces the analytically expected growth rates up to a density contrast of 10:1. The second part addresses the shear flow evolution with FLASH and PLUTO. Both codes result in a consistent non-viscous evolution (in the equal as well as in the different density case) in agreement with the analytical prediction. The viscous evolution studied with FLASH shows minor deviations from the analytical prediction.

Adaptive smoothed particle hydrodynamics and the simulation of large-scale structures formation

Journal of the Royal Astronomical Society of Canada, 1994

The development of a new Smoothed Particle Hydrodynamics (SPH) method, called Adaptive Smoothed Particle Hydrodynamics (ASPH), generalized for cosmology and coupled to the Particle Mesh (PM) method for solving the Poisson Equation, for the simulation of galaxy and large-scale structure formation, will be described. The accurate numerical simulation of the highly nonlinear phenomena of shocks and caustics which occur generically in the process of structure formation requires enormous dynamic range and resolution. Previously existing numerical methods require substantial modification in order to achieve the required resolution with current computer technology. The ASPH method incorporates new, adaptive, anisotropic smoothing and shock-tracking algorithms, which significantly enhance the resolving power of the• SPH method. We describe tests of ASPH versus SPH against the difficult cosmological pancake collapse problem. All cosmological hydro methods should be required to reproduce this test. High resolution 2D simulations of galaxy and large-scale structure formation in the Hot Dark Matter (HDM) model are presented using ASPH, showing that ASPH can resolve pancake shocks with fewer than 40 particles per pancake per dimension.

Adaptive Smoothed Particle Hydrodynamics: Methodology. II

The Astrophysical Journal Supplement Series, 1998

are presented. The ASPH method replaces the isotropic smoothing algorithm of standard SPH, in which interpolation is performed with spherical kernels of radius given by a scalar smoothing length, with anisotropic smoothing involving ellipsoidal kernels and tensor smoothing lengths. In standard SPH the smoothing length for each particle represents the spatial resolution scale in the vicinity of that particle, and is typically allowed to vary in space and time so as to reflect the local value of the mean interparticle spacing. This isotropic approach is not optimal, however, in the presence of strongly anisotropic volume changes such as occur naturally in a wide range of astrophysical flows, including gravitational collapse, cosmological structure formation, cloud-cloud collisions, and radiative shocks. In such cases, the local mean interparticle spacing varies not only in time and space, but in direction as well. This problem is remedied in ASPH, where each axis of the ellipsoidal smoothing kernel for a given particle is adjusted so as to reflect the different mean interparticle spacings along different directions in the vicinity of that particle. By deforming and rotating these ellipsoidal kernels so as to follow the anisotropy of volume changes local to each particle, ASPH adapts its spatial resolution scale in time, space, and direction. This significantly improves the spatial resolving power of the method over that of standard SPH at fixed particle number per simulation. This paper presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Paper I, based upon 1 Current Address: LLNL, L-16, Livermore, CA 94551 -2the Lagrangian deformation of ellipsoidal fluid elements surrounding each particle, is replaced by an approach involving a local transformation of coordinates to those in which the underlying anisotropic volume changes appear to be isotropic. Using this formulation the ASPH method is presented in 2D and 3D, including a number of details not previously included in Paper I, some of which represent either advances or different choices with respect to the ASPH method detailed in Paper I. Among the advances included here are an asynchronous time-integration scheme with different time steps for different particles and the generalization of the ASPH method to 3D. In the category of different choices, the shock-tracking algorithm described in Paper I for locally adapting the artificial viscosity to restrict viscous heating just to particles encountering shocks, is not included here. Instead, we adopt a different interpolation kernel for use with the artificial viscosity, which has the effect of spatially localizing effects of the artificial viscosity. This version of the ASPH method in 2D and 3D is then applied to a series of 1D, 2D, and 3D test problems, and the results are compared to those of standard SPH applied to the same problems. These include the problem of cosmological pancake collapse, the Riemann shock tube, cylindrical and spherical Sedov blast waves, the collision of two strong shocks, and problems involving shearing disks intended to test the angular momentum conservation properties of the method. These results further support the idea that ASPH has significantly better resolving power than standard SPH for a wide range of problems, including that of cosmological structure formation. Subject headings: cosmology: theory -galaxies: formation -hydrodynamicsintergalactic medium -large scale structure of the universe -methods: numerical

Tests of Spurious Transport in Smoothed Particle Hydrodynamics

1998

We have performed a series of systematic tests to evaluate the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numerical viscosity, and (iv) angular momentum transport. The results are useful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist & Katz, and by Balsara. For each form, our tests suggest a single set of values for the AV parameters α and β (coefficients of the linear and quadratic terms) which are appropriate in a large number of situations. We also discuss how these parameters should be adjusted depending on the goals of the particular application. We find that both the Hernquist & Katz and Balsara forms intro...

Towards a Mini-App for Smoothed Particle Hydrodynamics at Exascale

2018

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics represent computationallydemanding calculations. The parallelization of SPH codes is not trivial due to the absence of a structured grid. Additionally, the performance of the SPH codes can be, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. This work presents insights into the current performance and functionalities of three SPH codes: SPHYNX, ChaNGa, and SPHflow. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH miniapp. To gain such insights, a rotating square patch test was implemented as a common test simulation for the three SPH codes and analyzed on two modern HPC systems. Furthermore, to stress the differences with the codes stemming from the astrophysics community (SPHYNX and ChaNGa), an additional test case, the Evrard collapse, has also been carried out. This work extrapolates the common basic SPH features in the three codes for the purpose of consolidating them into a pure-SPH, Exascaleready, optimized, mini-app. Moreover, the outcome of this serves as direct feedback to the parent codes, to improve their performance and overall scalability.

Test of spurious transport in smoothed particle hydrodynamics

1999

We have performed a series of systematic tests to evaluate quantitatively the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numer-ical viscosity, and (iv) angular momentum transport. The effects of various program parameters on spurious mixing and on viscosity are investigated. The results are use-ful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. In particular, the particle diffusion coefficients we measure can be used to help estimate the spurious fluid mixing in SPH applications. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist and Katz, and by Balsara. Our tests suggest a single set of values for the AV parameters which are appropriate in a large number of sit...