Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

Abstract

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

“…In the medium Knudsen number regime, the S-model perform the best. For low speed Couette flow, we consider the case presented in [22]. Hard sphere model is adopted.…”

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

“…To investigate those complex nonequilibrium manifestations, a rigorous approach is to employ the Boltzmann equation [13][14][15][16][17][18][19][20] which describes the evolution of nonequilibrium statistical physical systems. However, solving the Boltzmann equation directly is computationally prohibitive.…”

Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes

“…By applying the above approaches, a number of flow problems from free molecular regime to continuum regime have been well resolved. Different from the above mentioned kinetic schemes [2][3][4][5][6][17][18][19][20][21][22][23][24], the semi-Lagrangian method [33][34][35] and lattice Boltzmann method (LBM) [36][37][38][39][40] have been devised and applied to simulate rarefied flows with streaming and collision processes. The semi-Lagrangian method is indeed a DVM.…”

“…In addition, the application of the semi-Lagrangian method for simulation of near continuum flows and hypersonic rarefied flows is still limited. As a powerful tool to solve the kinetic equation, the LBM has been extended to simulate rarefied flows by using the high-order LB models [36][37][38][39]. As indicated in [36], LBM can also be considered as a special form of DVM.…”

“…As a result, the present scheme can adjust the Prandtl number flexibly and capture the strong shock waves stably. As compared to the high-order LBM [36][37][38][39][40], the present scheme directly uses the complete Shakhov distribution function in the phase velocity space, and the Newton-Cotes quadrature is adopted to approximate the integrals of moments, which is capable to deal with highly non-equilibrium flows and high Mach number flows. However, large computational effort is needed for the present scheme since more points in the phase velocity space are required as compared with the high-order LBM.…”