An approximate two-dimensional Riemann solver for hyperbolic systems of conservation laws

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional solver is used to determine the solution of the equations at the cell vertices. The intercell fluxes are estimated using a linear combination between the point solutions at the cell vertices and the solutions of the one-dimensional problems at the centers of the cell interfaces. Besides allowing the computational time step to be increased the method gives more accurate results and is less sensitive to the anisotropy induced by the computational grid.