处理孔隙浅水模型中的几何不连续性
Coping with geometric discontinuities in porous shallow water models
AI总结：
针对单孔隙浅水模型在孔隙度突降处的黎曼解多重性问题，本文通过对照二维SWE数值解确定物理解及必要水头损失，并提出可选择一致解的近似黎曼求解器。
摘要：
在模拟浅水水流与障碍物之间的相互作用时，基于孔隙度的模型是经典二维（2-d）浅水方程（SWE）的一种可行替代方案。单孔隙（SP）黎曼问题是众多采用有限体积法求解的孔隙模型的构建基础；其精确解表现出一个有趣特征，即当超临界水流冲击突然的孔隙度降低时，解具有多重性。本文通过在局部孔隙度不连续处系统比较一维（1-d）SP黎曼问题的解与相应的二维SWE数值解，克服了这一歧义。该比较还得出另一项结果：在考虑强超临界水流时，SP黎曼问题应在穿过孔隙度不连续处时纳入适量的水头损失。一种近似黎曼求解器能够在多个备选解中选出物理上一致的解，并配备所需的水头损失量；当其在一维单孔隙有限体积格式中实现时，展现出良好的应用前景。
英文摘要：
Porosity-based models are a viable alternative to classical two-dimensional (2-d) Shallow water Equations (SWE) when the interaction of shallow flows with obstacles is modelled. The exact solution of the Single Porosity (SP) Riemann problem, which is the building block of numerous porosity models solved with the Finite Volume method, exhibits an interesting feature, namely the multiplicity of solutions when a supercritical flow impinges on a sudden porosity reduction. In the present paper, this ambiguity is overcome by systematically comparing the solution of the one-dimensional (1-d) SP Riemann problem with the corresponding 2-d SWE numerical solutions at local porosity discontinuities. An additional result of this comparison is that the SP Riemann problem should incorporate an adequate amount of head loss through porosity discontinuities when strongly supercritical flows are considered. An approximate Riemann solver, able to pick the physically congruent solution among the alternatives and equipped with the required head loss amount, shows promising results when implemented in a 1-d Single Porosity Finite Volume scheme.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
