Flux Globalization-Based Well-Balanced Path-Conservative Central-Upwind Scheme for Two-Dimensional Two-Layer Thermal Rotating Shallow Water Equations

I will introduce a flux globalization-based well-balanced path-conservative central-upwind scheme on Cartesian meshes for the two-dimensional (2-D) two-layer thermal rotating shallow water equations. The scheme is well-balanced in the sense that it can exactly preserve a variety of physically relevant steady states. In the 2-D case, preserving general "moving-water" steady states is difficult, and to the best of our knowledge, none of existing schemes can achieve this ultimate goal. The proposed scheme can exactly preserve the 𝑥- and 𝑦-directional jets in the rotational frame as well as certain genuinely 2-D equilibria. Numerical experiments demonstrate the performance of the proposed scheme in computationally non-trivial situations: in the presence of shocks, dry areas, non-trivial topographies, including discontinuous ones, and in the case of hyperbolicity loss. The scheme works equally well in both the 𝑓-plane and beta-plane frameworks.