Author(s): Chiang-An Hsu
Linked Author(s): Chiang-An Hsu
Keywords: Two-dimensional shallow water equations; Discontinuous flow; Multi-block finite-volume method; TVD/ENO shock-capturing scheme; LUSSOR; Runge-Kutt
Abstract: A general and powerful numerical model, named SEC-HY21, to compute the open-channel flows by solving the depth-averaged, two-dimensional unsteady shallow water equations is presented. The spatial solution algorithm used is a cell-centered multi-block finite-volume method in which the inviscid numerical fluxes are calculated by a class of high-resolution shock-capturing TVD (Total Variation Diminishing) and ENO (Essential Non-Oscillatory) schemes, and the viscous terms are evaluated with usual second-order accurate central difference. Several time-marching schemes including the second-order accurate Runge-Kutta explicit scheme and LUSSOR (Lower-Upper Symmetric Successive Over-Relaxation) implicit scheme that is distinguished for its computational efficiency as it needs only scalar diagonal inversions and is completely vectorizable on oblique planes of sweep are incorporated into the model. Two zero-equation eddy viscosity models, an empirical formula introduced by Fischer and a depth-averaged subgrid-scale model of Smagorinsky, and one depth-averaged standard model are available for resolving the turbulent flow. General and flexible boundary-condition setups and the treatment of drying/wetting and hydraulic structures are implemented. The model is capable of simulating smooth or discontinuous steady or unsteady flow conditions on complex shaped domains with complex topography. To assess the performance of the proposed model, both steady and unsteady smooth and discontinuous flows are simulated to verify its accuracy and robustness.
Year: 2001