Higher-order multi-dimensional limiting strategy for discontinuous Galerkin methods in compressible inviscid and viscous flows
초록
This paper deals with the multi-dimensional limiting process (MLP) for discontinuous Galerkin (DG) methods to compute compressible inviscid and viscous flows. The MLP, which has been quite successful in finite volume methods (FVM), is extended to DG methods for hyperbolic conservation laws. In previous works, the MLP was shown to possess several superior characteristics, such as the ability to control multidimensional oscillation efficiently and to capture both discontinuous and continuous multi-dimensional flow features accurately within the finite volume framework. In particular, the oscillation-control mechanism in multiple dimensions was established by combining the local maximum principle and the multidimensional limiting (MLP) condition, leading to the formulation of efficient and accurate MLP-u slope limiters.
