Investigation of the compact limiter based on discontinuous Galerkin methods

Use of high-order methods to convection-dominated transport problems tends to cause spurious oscillations and nonlinear instability in the approximate solution. To prevent the spurious oscillations, an improvement of the vertex-based hierarchical slope limiter was proposed in this paper. Local linear reconstruction is used to estimate upper and lower bounds for the values at all vertices of each element with only data of those neighbors with a common edge with the concerned element required to keep compactness of the scheme. For the higher-order approximate solutions, the hierarchical limiting strategy is used with the same compactness kept. The supposed improved vertex-based limiter is used with a discontinuous Galerkin method to several problems to verify its properties. The results show that the limiter can keep lower numerical dissipation, prevent spurious-oscillations while keeping compact.