The curve boundary design and performance analysis for DGM based on OpenFOAM

Abstract

OpenFOAM is a widely used numerical simulation software, and Discontinuous Galerkin method (DGM), a high-order numerical method, has been developed on OpenFOAM. In order to obtain meaningful numerical simulations, curve boundary is needed, but it has not been implemented on OpenFOAM. In this paper, based on codeStream function of original OpenFOAM, we design and implement curve boundary interface with reference to the interface of original OpenFOAM, so that users can use C++ code to describe curve boundary. Furthermore, in order to move the high-order points on the linear boundary to the curve boundary, we propose an algorithm to move each high-order point to a specific position on the curve, where the normal of this position passes through the origin point. Experimental results based on the flow around a cylinder show that curve boundary is needed by DGM numerical simulation, and DGM high-order simulation is much more efficient than DGM low-order. Typically, when the error of drag coefficient is about 0.03, the DGM high-order can save 89.6% time cost and 83.0% memory cost.