A New Class of Conservative Large Time Step Methods for the BGK Models of the Boltzmann Equation

Abstract

This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a Lagrangian formulation of the problem: information is stored on a fixed grid in space and velocity, and the equation is integrated along the characteristics. The source term is treated implicitly by using a DIRK (Diagonally Implicit Runge Kutta) scheme in order to avoid the time step restriction due to the stiff relaxation. In particular some L-stable schemes are tested by smooth and Riemann problems, both in rarefied and fully fluid regimes. Numerical results show good accuracy and efficiency of the method.

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• Conservative semi-Lagrangian schemes for kinetic equations Part II: Applications
• High order semi-Lagrangian methods for the BGK equation
• Semi-Lagrangian nodal discontinuous Galerkin method for the BGK Model
• Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model