Abstract
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.
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