A Simple Smoothing TVD Scheme on Structured and Unstructured Grids
A symmetric TVD Lax-Wendroff scheme is formulated via conservative smoothing or artificial viscosity. The approach is based on the Richtmyer scheme, a predictor-corrector Lax-Wendroff scheme. The predictor step is conducted at interface to determine the states there by advancing the Euler equations by modified half time step. The corrector step sums fluxes given by the Euler equations, and the smoothing flux given by artificial dissipation. The scheme is a simple central difference, and its artificial dissipation can be as less as the first-order upwind scheme around a discontinuity in solving the scalar equation. The scheme is extended to unstructured grid and applied to a variety of gas-dynamic problems by the finite volume method.
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