Finite Volume Subcell Shock Capturing for high order Discontinuous Galerkin methods
Discontinuous Galerkin methods of high order accuracy have the problem that shock waves travelling through grid cells introduce instabilities. The high order polynomial in coarse grid cell generates spurious oscillations when such an inner element jump has to be resolved. There exist different methods to circumvent these problems. One possible shock capturing, which is inspired by the finite volume methodology, is the approach of refining the grid in shock regions, while reducing the degree of the polynomials, often called hp-adaption. In general the reduction of the polynomial degree decreases the oscillations, while the resolution has to be preserved by the h-refinement.
In this talk a shock capturing for high order Discontinuous Galerkin methods is presented, which treates shock regions by Finite Volume techniques on a implicit subgrid. Due to the subcell approach the interior resolution on the Discontinuous Galerkin grid cells is preserved and the number of degrees of freedom remains the same, which enables a straightforward and fast implementation.