Well-balanced Finite difference WENO-AO scheme for rotating shallow water equations with Coriolis force. (English) Zbl 07833798
Summary: We develop an efficient conservative high-order well-balanced finite difference weighted essentially nonoscillatory (WENO) scheme for solving the rotating shallow water equations (SWEs) with Coriolis force. The scheme utilizes a well-balanced reconstruction proposed by Xing and Shu for the SWEs in [Y. Xing and C.-W. Shu, J. Comput. Phys. 208, No. 1, 206–227 (2005; Zbl 1114.76340)], combining with the idea of treating rotation as a topography from [F. Bouchut et al., J. Fluid Mech. 514, 35–63 (2004; Zbl 1067.76093)]. The finite difference WENO-AO(5,3) scheme is adopted, which selects from a large fifth-order centered stencil and three small third-order stencils in a weighted form for the reconstruction. Compared to a classical WENO scheme, the WENO-AO(5,3) scheme has a higher resolution, which makes it very effective for a long-time simulation. Numerical results are performed to demonstrate the good performance of our proposed approach for capturing small fine structures.
MSC:
| 76-XX | Fluid mechanics |
| 76U60 | Geophysical flows |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 35L65 | Hyperbolic conservation laws |
| 35L75 | Higher-order nonlinear hyperbolic equations |
Keywords:
Coriolis force; rotating shallow water equations; finite difference WENO; geostrophic equilibrium; high-resolutionSoftware:
chammpReferences:
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