High-Order Accurate Methods for High-Speed Flow

This work focuses on high-order numerical schemes for conservation laws with emphasis on problems that admit discontinuous solutions. We will investigate several enabling techniques with the aim to construct robust methods for unstructured meshes capable of reliably producing globally high-order accurate results even in the presence of discontinuities. We use spectral and pseudo-spectral schemes in connection with such techniques as Gibbs-complementary reconstruction to recover high-order accuracy near discontinuities.