Characteristic multigrid method application to solve the Euler equations with unstructured and unnested grids
The authors treat a new multigrid method for the solution of hyperbolic systems of conservation laws combined with higher order upwind approximation. The novelty of the method lies in the introduction of an upwind transfer between two successive grids. Part 2 of the paper presents the multigrid method with general transfer operators. Part 3 studies the sensitivity of the transfer operator upwinding for accelerating an explicit multistage iterative solver on a one-dimensional linear advection equation. Fourier analysis demonstrates the superiority of introducing upwinding. In part 4 of the paper the adaption of this approach to the two-dimensional geometric multigrid method is proposed in the unstructured mesh context. Finally numerical results with the new characteristic multigrid method applied to two-dimensional Euler flow computations illustrate the extended capacities of the algorithm. It allows the computation of severe problems such as hyperbolic flows with strong detached shocks. This was not possible with the classical approach.
scientific article; zbMATH DE number 168633