New two- and three-dimensional non-oscillatory central finite volume methods on staggered Cartesian grids

Central finite volume methods with constrained transport divergence treatment for ideal MHD

“…In the case of Cartesian grids, we also presented [6,8,10,11] a modified scheme introducing new oblique dual cells (''diamond cells'') instead of the dual cells with sides parallel to the coordinates axes originally considered in [2] for the second grid. These diamond cells were in fact the direct analogue of the quadrilateral dual cells introduced in the two-dimensional finite volume extension of the NT scheme described in [1,3] for unstructured triangular grids.…”

Central finite volume methods for ideal and shallow water magnetohydrodynamics

“…Both schemes are second-order accurate in the case of smooth solutions. It was shown in a previous work [21] that in the two-dimensional case, the diamond-staggered dual cell scheme is slightly more accurate than the Cartesian-staggered dual cell scheme. This may be explained by the fact that the area of the diamond dual cells is smaller than the area of the Cartesian dual cells, so that the resolution is better in the diamond-cell case.…”

“…Both schemes are secondorder accurate and are non-oscillatory thanks to van Leer's MUSCL-type limiters. A comparison between the diamond and the Cartesian dual cell schemes is presented in [21], where several problems in aerodynamics are considered. In this paper, we shall compare the numerical results for ideal MHD problems obtained using both versions of these two-dimensional central schemes.…”

Alleviation of cancellation problem of preconditioned Navier–Stokes equations

“…In order to get the flux vector at the surface of a grid cell, the preconditioned Roe's FDS (Flux Difference Splitting) scheme [17] with the third-order spatial accuracy is used. The van Albada limiter [18] is used to avoid numerical oscillations. The preconditioned LU-SGS (Lower Upper Symmetric Gauss Seidel) scheme [9,10] is used for time integration.…”