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.