带科里奥利源项的二维双曲系统的半离散Active Flux方法
Semi-discrete Active Flux method for two-dimensional hyperbolic systems with Coriolis source terms
- Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究半离散Active Flux方法在带科里奥利源项的二维浅水方程中保持地转平衡稳态的能力，通过离散傅里叶分析证明其固有保稳态特性，并数值验证线性和非线性系统性能。
AI中文摘要：
我们研究了在笛卡尔网格上应用于带科里奥利源项的二维线性和非线性浅水方程的半离散Active Flux数值方法。这些双曲系统允许由地转平衡控制的非平凡稳态解。在此背景下，我们分析了半离散Active Flux公式的保稳态性质。为此，对于线性系统，我们对半离散方法应用离散空间傅里叶变换，并分析所得的演化矩阵。我们证明其离散核是地转平衡的非平凡离散化，这意味着该方法保持离散地转平衡状态。这是Active Flux的固有特性，无需任何额外修改即可实现。数值实验证实了该方法对线性系统维持地转稳态的能力。此外，我们还数值研究了Active Flux方法对非线性浅水系统的性能。
英文摘要：
We investigate the semi-discrete Active Flux numerical method on Cartesian grids applied to two-dimensional linear and nonlinear shallow water equations with Coriolis source terms. These hyperbolic systems admit non-trivial stationary solutions governed by a geostrophic equilibrium. In this setting, we analyze the stationarity-preserving properties of our semi-discrete Active Flux formulation. To do so for the linear system, we apply a discrete spatial Fourier transform to the semi-discrete method and analyze the resulting evolution matrix. We show that its discrete kernel is a non-trivial discretization of the geostrophic equilibrium, which implies that the method preserves a discrete geostrophic equilibrium state. This is an inherent feature of Active Flux and is achieved without any additional modifications. Numerical experiments confirm the method's ability to maintain geostrophic stationary states for the linear system. Additionally, we numerically investigate the performance of the Active Flux method for the nonlinear shallow water system.
