Title: A high-resolution finite volume model for shallow water flow on uneven bathymetry using quadrilateral meshes Authors
|Kuiry, Soumendra -|
|Sen, Dhrubajyoti -|
|Ding, Yan -|
Submitted to: Computers & Fluids
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 21, 2012
Publication Date: September 1, 2012
Citation: Kuiry, S.N., Sen, D., Ding, Y. 2012. A high-resolution finite volume model for shallow water flow on uneven bathymetry using quadrilateral meshes. Computers & Fluids. 68:16-28. Interpretive Summary: In general, the two-dimensional (2D) shallow water equations are numerically solved to simulate many hydraulic and environmental engineering flow problems. Different numerical approaches such as the finite difference method, the finite element method, and the finite volume method have been employed to develop numerical simulation model of flood flows, dam-break flows, and levee breaching flows. The use of the finite volume technique has become more popular in recent years for simulating free surface flows because of its simplicity of implementation and good flexibility for space discretization. However, most existing flow models are based on rectangular grids in the Cartesian Coordinates, which unfortunately have limited their applications to solve flood flows over irregular topography and bathymetry in a large domain, due to lack of flexibility in grids. Development of a high-resolution flood flow model using unstructured grids is important to have adaptive resolution mesh to refine numerical grids over a local steep terrain. Triangular grids are commonly-used unstructured grids to obtain high-resolution flow results over a bottom-slope-varying bathymetry. However, quadrilateral grids are more attractive because of implementation of high-accurate numerical schemes and convenience in grid generation. The paper presents a high-resolution shallow water flow model, which is developed based on a cell-centred finite volume model and the HLL scheme on an unstructured quadrilateral mesh. This model is verified and validated by using analytical solutions and laboratory experimental data. This validated model would be a perfect tool to simulate complex flows like flood flows propagating in rivers, floodplains, and overlands. It is also useful for viscous flow computations on unstructured grids as the same computational stencil can be used for both the inviscid and viscous terms.
Technical Abstract: A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the HLL Riemann solver. An analytical proof is demonstrated to achieve exact balance between flux gradients and source terms whose implementation ensures well-balanced solution under still water conditions. A multidimensional gradient reconstruction procedure and a continuously differentiable multidimensional slope limiter based on a wide computational stencil are proposed in this study in order to maintain second-order spatial accuracy. The proposed model is verified by solving a wide variety of test cases having analytical solutions and laboratory observations.