TVD schemes for unstructured grids

High-order TVD shock-capturing schemes for unstructured grid solvers

A TVD principle and conservative TVD schemes for adaptive Cartesian grids

Modern high-resolution conservative numerical schemes (see [1–3]) are widely used for simulating flows of liquids, gases, or plasmas. They provide a robust and accurate method for capturing discontinuities, such as shock waves. A total-variation-diminishing (TVD) principle is an important element of such schemes. A TVD scheme is constructed in such a way that the total variation, TV 1⁄4 P ikUi ...

Generalised primal-dual grids for unstructured co-volume schemes

The generation of high-quality staggered unstructured grids for computational simulation is considered; leading to the development of a new optimisation-based strategy for the construction of weighted ‘RegularPower’ tessellations appropriate for co-volume type numerical techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble gen...

Three-Dimensional Adaptive Central Schemes on Unstructured Staggered Grids

We present a new formulation of three-dimensional central finite volume methods on unstructured staggered grids for solving systems of hyperbolic equations. Based on the Lax-Friedrichs and Nessyahu-Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve a staggered grids in order to avoid solving Riemann problems at cell interfaces. The cells are baryc...

Transonic Turbulent Flow Computations on Unstructured Triangular Grids