The Cartesian Grid Active Flux Method: Linear stability and bound preserving limiting

摘要

The primary contribution of this article is a linear stability analysis of the two-dimensional Cartesian grid Active Flux method. For the advection equation we show that stability for CFL ≤ 1 requires a more accurate flux computation than previously assumed. For the acoustic equations we confirm the expected stability for CFL≤12. Furthermore, we introduce a nonlinear limiting based on a bound preserving multi-dimensional reconstruction. Numerical results for advection and Burgers’ equation illustrate the performance of this limiting technique.