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A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates. (English) Zbl 1130.76051
Summary: A robust and accurate high-resolution finite volume scheme is presented which employs flux-vector splitting (FVS) as the building block for solution of shallow water equations in boundary-fitted curvilinear coordinates. Eddy viscosity approach is used to accommodate shear stresses due to turbulence. Splitting of convective terms is achieved via flux Jacobians whereas Liou-Steffen splitting technique, but in transformed coordinates, is used to split pressure terms. Limited flux gradients are also used to increase the computational accuracy of evaluation of interface fluxes and decrease the excessive numerical dissipation associated with FVS. This will completely remove spurious oscillations in high-gradient regions without introducing too much numerical dissipations. The method is tested for some classic simulations including hydraulic jump, 1D dam break and 2D dam break problems. The results show very satisfactory agreement with experimental data, analytical solutions and other numerical results.

76M12 Finite volume methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
86A05 Hydrology, hydrography, oceanography
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