Application of discontinuous Galerkin method in supersonic and hypersonic gas flows

摘要

Most high-order methods often suffer from two- and three-dimensional unstructured grids, particularly, for supersonic and hypersonic gas flows. We applied a high-order mixed-modal discontinuous Galerkin method with a coupled slope limiter to investigate multidimensional cases of supersonic and hypersonic gas flows. Furthermore, we provide detailed implementations and validations of two- and three-dimensional problems. Examples include double Mach reflection problems and supersonic and hypersonic gas flows around a cylinder. In addition, we provide case studies of a 3D hypersonic vehicle to evaluate its computational performance on complex hypersonic gas flows. This study can be regarded as an attempt to apply the discontinuous Galerkin method to engineering problems. (C) 2020 Elsevier Ltd. All rights reserved.