Spectral/hp methods for viscous compressible flows on unstructured 2D meshes (Q1287149)

A spectral/hp method suitable for simulating viscous compressible flows with shocks on standard unstructured meshes is developed. It is based on a discontinuous Galerkin formulation for the hyperbolic parts and a mixed Galerkin formulation for the diffusive parts. A hierarchical spectral basis is used for discretization. The basis is formed by combining Jacobi polynomials of high-order weights. The formulation is conservative, and monotonicity is enforced. Convergence results are shown for advection, Euler, and Navier-Stokes equations that demonstrate exponential convergence. Flow simulations of subsonic and supersonic flows are also presented. The new method uses standard finite volume meshes consisting of arbitrary triangulations.