浅水流动的可压缩流数学模拟

利用浅水流动的可压缩流比拟来认识浅水方程组的特性及其有关物理现象,过去的讨论多限于矩形断面棱柱形明渠的最简单情况。本文首先将该模拟推广到任意断面非棱柱形明渠的一般情况,给出了等价绝热指数公式γ=H/h.(H为水力水深,h_c为形心水深),并指出γ=2为矩形断面的特例.然后着重阐明这一数学模拟对计算水力学具有普遍实用价值,并将计算气体动力学中的两种通量向量分裂(FVS)算法通过比拟应用于浅水流动计算。最后,本文讨论了浅水流动可压缩流模拟与一般完全气体可压缩流物理特性的异同点,据此提出正确应用这一模拟所应遵循的原则。

Compressible-Fluid Flow Analogy of Shallow-Water Flows

It is time-honoured to understand tire properties of the shallow-water equations and related physical phenomena by analogy of a compressible-fluia flow.However, most of previous discussions were limited to the simplest case of.prismatic channels with a rectangular cross-section. In this paper, the analogy is extended to the general case of non-prismatic channels with an arbitrary cross-section. The equivalent adiabatic exponent γ=H/h_c (Where H is the hydraulic depth, and h_c is a height of the centroid above bottom) is given here, with γ=2 associated with the special case of rectangular cross-sections. Then, the practical importance of the gas dynamics analogy in computational hydraulics is emphatically expounded. Two fiuxvector-splitting (FVS) difference schemes used in CFD are applied to the shallow-water flow computation by tlhis analogy. Finally, the similarities and differences of physical behavior, between the compressible-fluid flow analogy of shallow-water flows and compressible-fluid flows of a perfect gas are highlighted, and guidelines that should be followed for a correct use of this analogy are proposed.