New high-resolution scheme for three-dimensional nonlinear hyperbolic conservation laws

We present a new third-order central weighted essentially non-oscillatory (CWENO) reconstruction for computations of nonlinear hyperbolic conservation laws in three spatial dimensions. The semi-discrete central-upwind schemes of Kurganov et al. are extended by giving some simple approximations for the local speeds of the discontinuities. To this end, the obtained CWENO-type central-upwind scheme, i.e., the extended semi-discrete central-upwind scheme based on the new high-resolution CWENO reconstruction, is developed straightforwardly to solve 3D systems, such as Euler equations and magnetohydrodynamics (MHD) equations. The good performance of the resulting method is finally shown in the numerical examples.