Fluid simulation using an adaptive semi-discrete central-upwing scheme

In this paper, we propose an adaptive semi-discrete central-upwind scheme on triangular meshes to approximate the solutions of hyperbolic conservation laws in gas dynamics: a local smoothness indicator is implemented to identify discontinuous solution regions; away from the discontinuities, a simple and computationally economical flux is used; near the discontinuities, an accurate but computationally uneconomical flux is used. Several numerical experiments, Euler equations and Kelvin-Helmholtz instability, are successfully simulated. The numerical results show the desired accuracy, high efficiency and robustness of the adaptive scheme.