Adaptive filtering and limiting in compact high order methods for multiscale gas dynamics and MHD systems

The adaptive multistep linear and nonlinear filters for multiscale shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows of the authors are extended to include compact high order central differencing as the spatial base scheme. The adaptive mechanism makes used of multiresolution wavelet decomposition of the computed flow data as sensors for numerical dissipative control. The objective is to expand the work initiated in [Yee HC, Sjögreen B. Nonlinear filtering in compact high order schemes. In: Proceedings of the 19th ICNSP and 7th APPTC conference; 2005; J Plasma Phys 2006;72:833–36] and compare the performance of adaptive multistep filtering in compact high order schemes with adaptive filtering in standard central (non-compact) schemes for multiscale problems containing shock waves.