A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods

This paper is devoted to the use of discontinuous Galerkin methods to solve hyperbolic conservation laws. The emphasis is laid on the elaboration of s lope limiters to enforce nonlinear stability for shock-capturing, The objec tives are to derive problem-independent methods that maintain high-order of accuracy in regions where the solution is smooth, and in the neighborhood of shock waves. The aim is also to define a way of taking into account high -order space discretization in limiting process, to make use of all the exp ansion terms of the approximate solution. A new slope limiter is first pres ented for one-dimensional problems and any order of approximation. Next, it is extended to bidimensional problems, for unstructured triangular meshes. The new method is totally free of problem-dependence. Numerical experiment s show its capacity to preserve the accuracy of discontinuous Galerkin meth od in smooth regions, and to capture strong shocks. (C) 2001 Academic Press .