High order semi-Lagrangian methods for the BGK equation
For researchers in computational gasdynamics, this provides more efficient high-order numerical schemes for solving the BGK model, though the approach is incremental.
The paper introduces high-order semi-Lagrangian methods for the BGK equation, demonstrating that BDF-based time integration is more efficient than DIRK, with numerical results confirming reliability across rarefied and fluid regimes.
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 gasdynamics.