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A New Spectral Difference Method for Conservation Laws Using Raviart-Thomas Elements

Investigator: Aravind Balan -- Advisor: Georg May


Numerical schemes using piecewise continuous polynomials are very popular for high order approximation of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not unconditionally linearly stable on triangles. We present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart-Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. Case studies are being conducted with this new Spectral Difference scheme where Euler equations are solved on unstructured grids.