Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grids

Abstract

The discontinuous Galerkin (DG) and spectral volume (SV) methods are two recently developed high-order methods for hyperbolic conservation laws capable of handling unstructured grids. In this paper, their overall performance in terms of efficiency, accuracy and memory requirement is evaluated using a 2D scalar conservation laws and the 2D Euler equations. To measure their accuracy, problems with analytical solutions are used. Both methods are also used to solve problems with strong discontinuities to test their ability in discontinuity capturing. Both the DG and SV methods are capable of achieving their formal order of accuracy while the DG method has a lower error magnitude and takes more memory. They are also similar in efficiency. The SV method appears to have a higher resolution for discontinuities because the data limiting can be done at the sub-element level. © 2004 John Wiley and Sons, Ltd.