Nonlinear filtering in compact high-order schemes

The adaptive nonlinear filtering approach for shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows adopted in our previous work is employed in conjunction with compact high-order methods as the spatial base scheme. The objective is to compare the performance of nonlinear filtering in compact high-order schemes with nonlinear filtering in standard central (non-compact) schemes for multiscale problems containing shock waves.