| Abstract: |
| In this talk, we introduce finite difference high order conservative semi-Lagrangian schemes for the ellipsoidal BGK model of the Boltzmann equation. To avoid the time step restriction induced by the convection term, we adopt the semi-Lagrangian approach. For treating the nonlinear stiff relaxation operator with small Knudsen number, we employ high order $L$-stable diagonally implicit Runge-Kutta time discretization or backward difference formula. The proposed implicit scheme is designed to update solutions explicitly without resorting to any Newton solver. We present several numerical tests to demonstrate the accuracy and efficiency of the proposed method. In particular, we show that our method is able to capture the behavior of Navier-Stokes equations for moderate values of Knudsen number, and provide good approximation of the solution to Boltzmann equation for relatively large values of Knudsen number. |
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