A Finite Volume Method for Large-Eddy Simulation of Shallow Water Equations

We present a robust finite volume method for large-eddy simulation of shallow water flows. The governing equations are derived from the Navier-Stokes equations with assumptions of shallow water flows including bed frictions and eddy viscosity. The turbulence effects are incorporated in the system by considering the Smagorinsky model. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix of the convective part of the large-eddy shallow water equations. The diffusion terms are discretized using a Green-Gauss diamond reconstruction. The proposed method is verified for the benchmark problem of flow around a circular cylinder.