NUMERICAL PREDICTION OF SUB - AND SUPER - CRITICAL FLOWS BY SHALLOW WATER EQUATIONS WITH MACS

Abstract

A computational method has been proposed for shallow water equations, which is based on the prediction method for incompressible fluids on collocated grid system. In the proposed method, called MACS (MAC method on Collocated grid for Shallow water equations), the momentum equations are discretized with a C-ISMAC method and the water depth h is treated implicitly. The continuity equation is also discretized implicitly and its numerical solutions for φ = hⁿ⁺¹-hⁿ are obtained by solving simultaneous equations. The unit flow rates are corrected with the iterative computations based on the C-HSMAC method. The new treatment for the continuity equation is proposed and it enables us to predict dam-break problems, hydraulic jumps and sub-and super-critical flows stably and accurately without artificial diffusions.