Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems

In this paper, the fourth in a series, the spectral volume (SV) method is extended to multi-dimensional systems – the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems, and to verify that high order solution accuracy up to fourth-order can be achieved for the systems of conservation laws. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. An accuracy study is performed first to numerically verify that the designed order of accuracy can be obtained for smooth flow solutions. Then, solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.