Communications in Mathematical Sciences
Volume 14 (2016)
High order semi-Lagrangian methods for the BGK equation
Pages: 389 – 414
A new class of high-order accuracy numerical methods for the BGK 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.
Boltzmann equation, BGK equation, semi-Lagrangian methods, high-order schemes
2010 Mathematics Subject Classification
65L06, 65M25, 76P05