AN OPTIMALLY ACCURATE SPECTRAL VOLUME FORMULATION WITH SYMMETRY PRESERVATION

Abstract

High order accuracy has become a challenge in numerical simulations for engineering applications. A number of methods have been developed which provide adequate levels of accuracy in numerical simulations. Among them, the Spectral Volume (SV) method is the most effective approach that ensures local conservation and achieves high order accuracy for unstructured grids. A number of formulations for SV method have been reported and tested. However, these formulations are inconsistent and/or do not preserve the symmetry property of an elliptical operator. In this paper, we propose a new formulation, named as Symmetry Preservation in Spectral Volume (SPSV) for spectral volume method that is not only consistent and stable, but also preserves the symmetry property of an elliptical operator. We test the newly proposed formulation on diffusion equation and Burger equation using different boundary conditions and evaluate it with respect to symmetry preserving capability, accuracy, and stability. Furthermore, we also present a detailed comparison between the local SV and the SPSV formulation. Our results show that besides preserving the symmetry of an elliptical operator, the SPSV formulation is more accurate and stable.