Role of Artificial Dissipation Scaling and Multigrid Acceleration in Numerical Solutions of the Depth-Averaged Free-Surface Flow Equations

Abstract

A numerical model is developed for solving the depth-averaged, open-channel flow equations in generalized curvilinear coordinates. The equations are discretized in space in strong conservation form using a space-centered, second-order accurate finite-volume method. A nonlinear blend of first- and third-order accurate artificial dissipation terms is introduced into the discrete equations to accurately model all flow regimes. Scalar- and matrix-valued scaling of the artificial dissipation terms are considered and their effect on the accuracy of the solutions is evaluated. The discrete equations are integrated in time using a four-stage explicit Runge–Kutta method. For the steady-state computations, local time stepping, implicit residual smoothing, and multigrid acceleration are used to enhance the efficiency of the scheme. The numerical model is validated by applying it to calculate steady and unsteady open-channel flows. Extensive grid sensitivity studies are carried out and the potential of multigrid acceleration for steady depth-averaged computations is demonstrated.