A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method (Communications in Computational Physics, 2018)
The finite volume (FV) method is the dominating discretization techniquefor computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method atlowest order. However, many of today’s CFD codes use a vertex-centered FV methodin which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the newscheme for scalar hyperbolic problems. Numerically, the method shows optimal-orderaccuracy for a smooth linear problem. By applying a basic hp-adaption strategy, themethod successfully handles shocks. We also discuss how to extend the FV edge-baseddata structure to support the new scheme. In this way, it will in principle be possible toextend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.