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水力发电学报

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非反射开放边界在SWE-SPH模型中的实现

  

  • 出版日期:2024-12-17 发布日期:2024-12-17

Implementation of Non-Reflective Open Boundary Conditions in SWE-SPH Method

  • Online:2024-12-17 Published:2024-12-17

摘要: 使用光滑粒子流体动力学(SPH)求解浅水方程(SWE)在海洋数值模拟领域具有巨大潜力,然而SWE-SPH方法中开放边界还存在许多问题仍未解决。本研究针对现有SWE-SPH模型中开放边界的反射问题,基于Flather的重力波开放边界理论,提出了新的非反射边界处理方法。通过凸起地形定常流动、双开口平底通道海平面扰动和圆柱绕流三个案例,评估了新边界条件的性能,并与原方法中的特征开放边界条件进行对比。结果表明新边界能有效减少反射,允许扰动向外传播,且易于通过模型开放边界处指定的外部流动条件实现。此外将SWE-SPH模型应用于Okushiri海啸模拟,并与有限体积法结果对比,验证了模型在复杂水深跨临界流动中的适用性和有效性,以模拟更广泛的海洋数值模拟问题。

Abstract: The application of Smoothed Particle Hydrodynamics (SPH) in solving the Shallow Water Equations (SWE) holds significant potential. This potential is particularly evident in the field of ocean numerical simulation. However, issues related to open boundaries in the SWE-SPH method remain unresolved. This study addresses the reflection problem at open boundaries in existing SWE-SPH models. It proposes a new non-reflective boundary treatment method based on Flather's theory of gravity wave open boundaries. The performance of the new boundary condition is evaluated using three classic numerical simulation cases: steady flow over a bump, propagation of sea level perturbations in a flat-bottom channel with two open ends, and circular cylinder. Comparisons are made with the characteristic open boundary conditions from the original method. Results indicate that the new boundary conditions effectively reduce reflections, allow disturbances to propagate outward, and facilitate the implementation of external flow conditions specified at the model's open boundaries. Furthermore, the SWE-SPH model has been applied to simulate the Okushiri tsunami. The simulation results were then compared with those from the finite volume method. This comparison demonstrates the model's applicability and effectiveness in handling complex depth and transcritical flow simulations, thus expanding the scope of ocean numerical simulation problems that can be addressed.

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