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首页> 外文期刊>Journal of Engineering Mechanics >Applying the Method of Characteristics and the Meshless Localized Radial Basis Function Collocation Method to Solve Shallow Water Equations
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Applying the Method of Characteristics and the Meshless Localized Radial Basis Function Collocation Method to Solve Shallow Water Equations

机译：应用特征方法和无网局部径向基函数搭配方法解决浅水方程

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摘要

This paper proposes an accurate and efficient numerical model by combining the method of characteristics (MOC) and the meshless localized radial basis function collocation method (LRBFCM) to simulate the shallow water flow problems. The shallow water equations (SWEs) are classified into a hyperbolic-type partial differential equations (PDEs) system that easily creates numerically unstable results for the case with discontinuous field values or shock waves. To solve this problem, the SWEs are derived into conservative eigensystem form, and then the MOC is applied to capture the change of conservative variables along the characteristic lines. Specifically, the meshless LRBFCM is used to obtain the field values from the conservative variables; it can ease the complexity of the interpolation procedure on characteristic Lagrangian points and preserve the accuracy in transient problems. For the boundary disposal, a fractional time step skill with the characteristic velocity is considered to determine the boundary requirements. The computational nodes can be generated by the uniform or nonuniform distribution, which reduces the difficulty of node generation to obtain efficient and accurate numerical analysis. Six continuous and discontinuous SWEs benchmark examples are simulated and discussed to verify the proposed model. The excellent agreements with the analytical, experimental, and numerical solutions demonstrate the accuracy and efficiency of the algorithm.
机译：本文通过将特性（MOC）和无网格局部径向基函数搭配方法（LRBFCM）组合来提出一种准确和有效的数值模型来模拟浅水流量问题。浅水方程（SWES）分为一个双曲线型部分微分方程（PDES）系统，该系统容易为具有不连续的场值或冲击波的情况创建数值不稳定的结果。为了解决这个问题，SWES衍生给保守的EIGensystem形式，然后应用MOC以捕获沿着特征线的保守变量的变化。具体地，无网格LRBFCM用于从保守变量获得场值;它可以缓解插值过程对特征拉格朗日点的复杂性，并保持瞬态问题的准确性。对于边界处理，认为具有特征速度的分数时间步长技巧以确定边界要求。计算节点可以由均匀或非均匀分布产生，这减少了节点生成的难度，以获得有效和准确的数值分析。模拟并讨论了六个连续和不连续的SWES基准示例以验证所提出的模型。与分析，实验和数值解决方案的良好协议展示了算法的准确性和效率。

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