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For the two-layer shallow water equations, a high-order compact gas-kineticscheme (GKS) on triangular mesh is proposed. The two-layer shallow waterequations have complex source terms in comparison with the single layerequations. The main focus of this study is to construct a time-accurateevolution solution at a cell interface and to design a well-balanced scheme.The evolution model at a cell interface provides not only the numerical fluxes,but also the flow variables. The time-dependent flow variables at the closedcell interfaces can be used to update the cell-averaged gradients for thediscretization of the the source terms inside each control volume in thedevelopment of the well-balanced scheme. Based on the cell-averaged flowvariable and their gradients, high-order initial data reconstruction can beachieved with compact stencils. The compact high-order GKS has advantages tosimulate the flow evolution in complex domain covered by unstructured mesh.Many test cases are used to validate the accuracy and robustness of the schemefor the two-layer shallow water equations.

High-order Compact Gas-kinetic Scheme for Two-layer Shallow Water Equations on Unstructured Mesh