Well-Balanced Path-Conservative Central-Upwind Schemes Based on Flux Globalization

We study non-conservative hyperbolic systems of balance laws and are interested in development of well-balanced (WB) numerical methods for such systems. One of the ways to enforce the balance between the flux terms and source and non-conservative product terms is to rewrite the studied system in a quasi-conservative form by incorporating the latter terms into the modified global flux. The resulting system can be quite easily solved by Riemann-problem-solver-free central-upwind (CU) schemes. This approach, however, does not allow to accurately treat non-conservative products. We therefore apply a path-conservative (PC) integration technique and develop a very robust and accurate path-conservative central-upwind schemes (PCCU) based on flux globalization. I will demonstrate the performance of the WB PCCU schemes on a wide variety of examples.