论文标题
稳定实现了良好的二维曲线浅水方程，没有渗透壁和远场边界条件
A Stable Implementation of a Well-posed 2-D Curvilinear Shallow Water Equations with No-Penetration Wall and Far-Field Boundary conditions
论文作者
论文摘要
本文介绍了更稳定的实施和一种高度准确的数值工具，用于预测城市地区的洪水。我们从[1]开始从（线性化的）适当性分析开始，其中提出了远场边界条件，但扩展了其分析以包括壁边界。具体而言，采用有限差异操作员逐个局部求和（SBP）来构建浅水方程的方案。随后，开发了具有同时构成远场和壁边界的同时近似项的稳定SBP方案。最后，我们将方案及其稳定性证明扩展到了非 - 卡特斯域。为了证明方案的强度，进行了精确溶液问题的计算，并具有第二，第三和第四（2,3,4）收敛速率的理论设计顺序。最后，我们将四阶方案应用于稳定的河道，运河（或洪水控制通道模拟）和大坝破裂问题。结果表明，边界条件的强加是稳定的，并且在边界上没有可见的反射。在洪水风险管理决策中，该分析非常有必要，因为它们可以确认洪泛区变量的稳定且准确的未来预测
This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed but extended their analysis to include wall boundaries. Specifically, high-order Summation-by-parts (SBP) finite-difference operators were employed to construct a scheme for the Shallow Water Equations. Subsequently, a stable SBP scheme with Simultaneous Approximation Terms that imposes both far-field and wall boundaries was developed. Finally, we extended the schemes and their stability proofs to non-cartesian domains. To demonstrate the strength of the schemes, computations for problems with exact solutions were performed and a theoretical design-order with second-, third- and fourth (2,3,4) convergence rates obtained. Finally, we apply the 4th-order scheme to steady river channel, canal (or flood control channel simulations), and dam-break problems. The results show that the imposition of the boundary conditions are stable, and that they cause no visible reflections at the boundaries. The analysis adequately becomes necessary in flood risk management decisions since they can confirm stable and accurate future predictions of floodplain variables
