HIGH ORDER SEMI-LAGRANGIAN METHODS FOR THE BGK EQUATION

摘要

A new class of high-order accuracy numerical methods for the BGR model of the Boltzmann equation is presented. The schemes are based on a semi-Lagrangian formulation of the BGK equation; time integration is dealt with DIRK (Diagonally Implicit Runge-Kutta) and BDF methods; the latter turn out to be accurate and computationally less expensive than the former. Numerical results and examples show that the schemes are reliable and efficient for the investigation of both rarefied and fluid regimes in gas dynamics.