Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes |
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| Authors: | X Liu BJ Landry MH García |
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| Institution: | Ven Te Chow Hydrosystems Laboratory, Department of Civil and Environmental Engineering, University of Illinois at Urbana and Champaign, 205 N Mathews Ave., Urbana, IL, 61801, USA |
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| Abstract: | A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments. |
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| Keywords: | Shallow water equations Sediment transport Godunov scheme Coupled solver Unstructured mesh |
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