Abstract
The present study makes efforts to simulate the behavior of fully developed stationary shocks, caused by the incidence of supercritical flow with a cross-barrier in an open channel. The numerical solution of nonlinear governing shallow flow equations has been implemented by the application of a second-order Roe TVD scheme. The obtained results from numerical experiment are compared with some measured in a laboratory setup. It can be deduced by comparison of the flow depths in numerical and measured experiments in three different cases of cross-barrier width of 6, 12 and 16 cm that the numerical scheme of Roe is a robust and capable method for simulation of complicated stationary shocks in shallow water flow.
Highlights
When an abrupt change occurs in flow depth and/or velocity, the shocks or bores will appear
The shocks normally appear in supercritical flows, while transition from super- to the subcritical regime, named trans-critical, can produce a shock
They are divided into two general categories: dynamic shocks whose characteristics are various over time and static shocks whose locations and other characters are permanent after the flow steady state
Summary
When an abrupt change occurs in flow depth and/or velocity, the shocks or bores will appear. The shocks normally appear in supercritical flows, while transition from super- to the subcritical regime, named trans-critical, can produce a shock (i.e., hydraulic jump). The governing equations on shock simulation problem are the shallow flow equations. Since the early days of the 1980s, the idea of Godunov conservative method has been in application for the solution of Euler equation. These methods are not capable of capturing sharp discontinuities such as shock and bores without employing numerical viscosity or simplifications of governing equations.
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