Particle-based fluid dynamics: comparison of different BGK models and DSMC for hypersonic flows

Abstract

The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this end, different methods are investigated that allow efficient sampling of the Shakhov and the unified target distribution functions. As a consequence, particle simulations based on the Shakhov BGK and the unified BGK model are possible in an efficient way. Furthermore, different energy conservation schemes are tested for the BGK models. It is shown that the choice of the energy conservation scheme has a major impact on the quality of the results for each model. The models are verified with a Couette flow problem at different Knudsen numbers and wall velocities. Furthermore, the models are compared with DSMC results of a hypersonic flow around a 70${}^{\circ }$ blunted cone. It is shown that the unified BGK model is able to reproduce rarefied gas phenomena. Furthermore, it is shown that the difference in the reproduction of shock structure is not significant between the ellipsoidal statistical BGK and Shakhov BGK model for the flow around a 70${}^{\circ }$ blunted cone and significantly depends on the energy conservation method. The choice of the energy conservation method is especially crucial for the Shakhov model whereas the ellipsoidal statistical BGK model is much more robust concerning the energy conservation scheme. Additionally, a computational time study is done to show the efficiency of BGK-based simulations for low Knudsen number flows compared with DSMC.

References in corpus (1)

• A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

Cited by in corpus (11)

• Simplified Unified Wave-Particle Method with Quantified Model-Competition Mechanism for Numerical Calculation of Multi-Scale Flows
• Extending the Particle ESBGK Method to Diatomic Molecules including Quantized Vibrational Energies
• Optimisation of VLEO Satellite Geometries for Drag Minimisation and Lifetime Extension
• Exponential BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations
• An ES-BGK model for diatomic gases with correct relaxation rates for internal energies
• Multi-species modeling in the particle-based ESBGK method for monatomic gas species
• A unified stochastic particle method based on the Bhatnagar-Gross-Krook model for polyatomic gases and its combination with DSMC
• Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method including internal degrees of freedom
• A direct relaxation process for particle methods in gas kinetic theory
• Hybrid Parallelization of Euler-Lagrange Simulations Based on MPI-3 Shared Memory
• Implementation of Asymptotic Preserving Discrete Velocity Methods into the Simulation Code PICLas