Journal Article10.1002/FLD.1650160706
Flux difference splitting for open‐channel flows
73
TL;DR: In this paper, a finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows.
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Abstract: A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.
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An approximate linearised Riemann solver for the Euler equations for real gases
TL;DR: In this paper, an approximate Riemann solver is presented for the solution of the Euler equations of gas dynamics in one dimension with a general convex equation of state, applied to a standard shock reflection test problem for some specimen equations of state.
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