On some numerical dissipation schemes

Several schemes for introducing an artificial dissipation into a central di fference approximation to the Euler and Navier-Stokes equations are conside red. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dis sipation and matrix dissipation (MATD) schemes. Resolution capability is de termined by solving subsonic, transonic, and hypersonic flow problems. A fi nite-volume discretization and a multistage time-stepping scheme with multi grid are used to compute solutions to the flow equations. Numerical solutio ns are also compared with either theoretical solutions or experimental data , For transonic airfoil flows the best accuracy on coarse meshes for aerody namic coefficients is obtained with a simple MATD scheme. The coarse-grid a ccuracy for the original CUSP scheme is improved by modifying the limiter f unction used with the scheme, giving comparable accuracy to that obtained w ith the MATD scheme. The modifications reduce the background dissipation an d provide control over the regions where the scheme can become first order. (C) 1998 Academic Press.