Efficient Finite-Volume Model for Shallow-Water Flows Using an Implicit Dual Time-Stepping Method

Abstract

An implicit dual time-stepping method (DTS) is applied to a Godunov-type finite-volume model for two-dimensional (2D) shallow-water flows on unstructured grids to improve run-time efficiency. In this model, an implicit nonlinear lower–upper symmetric Gauss–Seidel (LU-SGS) solution algorithm is used as an inner iteration solver for DTS. To relieve the quantity nonconservation problem of DTS, a water quantity conservation correction method is presented. Five extensive test cases including two analytical benchmark cases and experimental and actual dam-break cases have been applied to validate the proposed model and to demonstrate its performance by comparison with an explicit scheme. The presented results show that DTS can reduce the run time from 55 to 78% without or with a minimal loss of accuracy. The overall performance demonstrates that the proposed model is accurate and efficient for simulating shallow water in practical applications.