Second-Order Fully Discrete Central-Upwind Scheme for Two-Dimensional Hyperbolic Systems of Conservation Laws.

In this paper, we derive a new second-order fully discrete Godunov-type central-upwind scheme for two-dimensional hyperbolic systems of conservation laws. The scheme is derived in three steps: reconstruction, evolution, and projection. The novelty of our approach is in the evolution step, which is performed using the nonuniform quadrilateral control volumes obtained based on the one-sided local speeds of propagation, and in the projection step, in which the evolved solution is projected back onto the uniform grid with the help of a new sharp piecewise polynomial reconstruction. The scheme is tested on a number of numerical examples for the Euler equations of gas dynamics. We have demonstrated that the new scheme is nonoscillatory and at the same time it achieves higher resolution than the second-order semidiscrete central-upwind scheme. The latter suggests that the fully discrete scheme has a smaller amount of numerical dissipation.