Investigation of a slope limiter for Runge-Kutta discontinuous Galerkin methods

A new slope limiter was formulated for the discontinuous Galerkin methods in this paper. Unlike the previous slope limiters,this slope limiter reconstructed the new gradients for limiting by using the total differential method and took no account of the element types.Consequently,it can be adopted on structured grids,pure-element unstructured grids and mixed-element unstructured grids,leading to a versatile limiter to resolve more effectively complex geometry problems.The developed slope limiter was used in a discontinuous Galerkin method to compute a variety of flow problems.The numerical results show its capability to different types of elements,to preserve the accuracy in smooth regions as well as to prevent spurious oscillations near solution discontinuities.