High-order-accurate numerical method for complex flows

A numerical method employing high-order-accurate (higher than third) upwind discretizations for solving the compressible Navier-Stokes equations on structured grids is discussed. The inviscid fluxes are computed by a procedure based on a weighted essentially nonoscillatory interpolation of the characteristic variables and the Roe scheme. Application of the numerical method to a number of test cases of increasing complexity, that are prototypical for several of the key aspects of practical flows, demonstrates the accuracy and robustness of the method even when computing on distorted curvilinear grids. Significant reductions in computer time are possible when a second-order-accurate implicit Adams-Moulton scheme is employed for time integration. The combination of implicit time integration and high-order-accurate spatial discretization is shown to lead to significant savings in compute time as the grid resolution requirement is lowered and the time step can be increased.