Flux Limiters for Mixed Element Volume Scheme
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Flux limiters are used in numerical schemes to prevent spurious oscillations and ensure the Total Variation Diminishing (TVD) property, so that no local extrema are generated by the scheme. This causes an injection of numerical dissipation inside the computation, whose drawbacks are the loss of accuracy and possible convergence stalls in smooth regions of the solution. This gives motivation to perform an analysis on different limiting strategies, in order to reduce the amount of dissipation that is added in the scheme. In the Wolf solver, a Mixed Element Volume scheme is used to discretize the Reynolds Averaged Navier- Stokes (RANS) equations. The convective fluxes are discretized with a node-centered Finite Volume scheme. The flux balance for each vertex is computed with an integral on the boundary of the finite volume cell, decomposed in the interfaces between the vertex and its neighbors. Each interface is associated with an edge, and the corresponding flux is computed by solving a one-dimensional Riemann problem in the direction of the normal to the interface. To achieve higher order, Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) reconstructions are done, using the V4 scheme to compute gradients that are multiplied to a limiter function. Thanks to the mono-dimensional approach of the scheme, classical limiters can be used. An extension of the Van Albada limiter called Gamma limiter is used in the solver, and is tuned using a parameter. In this work, the limiter will be optimized, in order to inject the minimum quantity of dissipation, while keeping the limiter in the TVD region. An alternative approach is to associate a flux limiter to the vertex. Limiters of this type will be tested, as the ones proposed by Nishikawa. The comparison will be made on different test cases.
