Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates

Abstract

The entropy conservative/stable staggered grid tensor-product algorithm of Parsani et al. [1] is extended to multidimensional SBP discretizations. The required SBP preserving interpolation operators are proven to exist under mild restrictions and the resulting algorithm is proven to be entropy conservative/stable as well as elementwise conservative. For 2-dimensional simplex elements, the staggered grid algorithm is shown to be more accurate and have a larger maximum time step restriction as compared to the collocated algorithm. The staggered algorithm significantly reduces the number of (computationally expensive) two-point flux evaluations, which is potentially important for both explicit and implicit time-marching schemes. Furthermore, the staggered algorithm requires fewer degrees of freedom for comparable accuracy, which has favorable implications for implicit time-marching schemes.