A variant of Van Leer's method for multidimensional systems of conservation laws (Q1331448)

A new variant of Van Leer's construction of upwind finite volume schemes for solving multidimensional hyperbolic systems of conservation laws on unstructured grids is presented. Fluxes are computed with second-order accuracy using an interpolation rather than a slope reconstruction. A correction of the interpolated values is necessary and performed globally on each cell by a conservation argument. It is proved that the second-order reconstruction, combined with a Boltzmann solver, gives nonnegative values of the pressure and density for gas dynamics equations. This leads us to derive a rigorous CFL condition. Several numerical tests are presented.