2023/06/07 by Fengxiang Zhao, Zhao, Fengxiang, Jianping Gan +3 · 2 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2306.04467
openalex publication_date 2023/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the two-layer shallow water equations, a high-order compact gas-kinetic scheme (GKS) on triangular mesh is proposed. The two-layer shallow water equations have complex source terms in comparison with the single layer equations. The main focus of this study is to construct a time-accurate evolution 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 closed cell interfaces can be used to update the cell-averaged gradients for the discretization of the the source terms inside each control volume in the development of the well-balanced scheme. Based on the cell-averaged flow variable and their gradients, high-order initial data reconstruction can be achieved with compact stencils. The compact high-order GKS has advantages to simulate the flow evolution in complex domain covered by unstructured mesh. Many test cases are used to validate the accuracy and robustness of the scheme for the two-layer shallow water equations.