A High-Order Unifying Discontinuous Formulation for 3D Mixed Grids

The newly developed unifying discontinuous formulation based on flux reconstruction and lifting collocation penalty (LCP) approaches for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The LCP formulation is an extension of the flux reconstruction (FR) method to arbitrary element types. As with the FR method, it can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form without any explicit integration. By selecting the solution points to coincide the flux points, solution reconstruction can be completely avoided. Numerical accuracy of the scheme is assessed for grid refinement studies. Several typical test cases are computed by solving the Euler equations and the compressible Navier-Stokes equations to demonstrate its performance.