The semi-discrete Active Flux method is proven stationarity preserving for multi-dimensional linear acoustics on Cartesian grids, with explicit kernel bases and a 2D CFL limit near 0.28.
Stationarity preserving schemes for multi-dimensional linear systems
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Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform
The semi-discrete Active Flux method is proven stationarity preserving for multi-dimensional linear acoustics on Cartesian grids, with explicit kernel bases and a 2D CFL limit near 0.28.