Abstract
This paper presents a two-dimension (2-D) numerical model for simulating dam-break flow involving wet-dry fronts over irregular topography. The Central- upwind scheme is chosen to calculate interface fluxes for each cell edge. A second order spatial linear reconstruction with multidimensional limiter and second order TVD Runge-Kutta scheme are chosen to acquire high order accuracy in space and time. Non-negative water reconstruction of variables at cell interfaces and compatible discretization of slope source term lead to stable and well-balanced scheme for hydraulics over irregular topography. The friction term is discretized with a semi-implicit scheme for numerical stability when very small water depth exists. An accurate and effective technique is presented for tracking wetting-drying interfaces during the process of wave front propagation on dry bed. The capacity and accuracy of current model are verified by several benchmark tests as well as a real dam-break case, and good performances are achieved in tests.
Highlights
Dam-break flows over irregular bed often experience the cases as transcritical flows, steep bed slope, very small water depth, cells’ wetting and drying, wave propagation
The coupled system is discretized on an unstructured triangular grid by finite volume method
Since the topography is set to be frictionless in this test, as described in [15], the periodic analytical solution of the evolutions of surface elevation, water depth and velocities can be computed using following equations: η(x, y, t) h(x, y, t) = max[0, η(x, y, t) − Z(x, y)], u(t) = −ωσsin(ωt), v(t) = ωσcos(ωt) in which, σ is a constant that determines the amplitude of the motion; ω = √2gh0/a2 is the frequency of the pool’s circulation around the center of the bowl
Summary
Abstract- This paper presents a two-dimension (2-D) numerical model for simulating dam-break flow involving wet-dry fronts over irregular topography. The Centralupwind scheme is chosen to calculate interface fluxes for each cell edge. A second order spatial linear reconstruction with multidimensional limiter and second order TVD Runge-Kutta scheme are chosen to acquire high order accuracy in space and time. Non-negative water reconstruction of variables at cell interfaces and compatible discretization of slope source term lead to stable and well-balanced scheme for hydraulics over irregular topography. The friction term is discretized with a semi-implicit scheme for numerical stability when very small water depth exists. The capacity and accuracy of current model are verified by several benchmark tests as well as a real dam-break case, and good performances are achieved in tests. Unrestricted use, distribution, and reproduction in any medium are permitted, provided the original work is properly cited
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