Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
Journal of Computational Physics
High resolution finite volume methods on arbitrary grids via wave propagation
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Use of a rotated Riemann solver for the two-dimensional Euler equations
Journal of Computational Physics
An unsplit 3D upwind method for hyperbolic conservation laws
Journal of Computational Physics
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
A second-order unsplit Godunov scheme for two- and three-dimensional Euler equations
Journal of Computational Physics
Two-dimensional Riemann solver for Euler equations of gas dynamics
Journal of Computational Physics
Hi-index | 31.45 |
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.