Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 5
Abstract
A total variation diminishing Runge Kutta discontinuous Galerkin finite-element method for two-dimensional depth-averaged shallow water equations has been developed. The scheme is well suited to handle complicated geometries and requires a simple treatment of boundary conditions and source terms to obtain high-order accuracy. The explicit time integration, together with the use of orthogonal shape functions, makes the method for the investigated flows computationally as efficient as comparable finite-volume schemes. For smooth parts of the solution, the scheme is second order for linear elements and third order for quadratic shape functions both in time and space. Shocks are usually captured within only two elements. Several steady transcritical and transient flows are investigated to confirm the accuracy and convergence of the scheme. The results show excellent agreement with analytical solutions. For investigating a flume experiment of supercritical open-channel flow, the method allows very good decoupling of the numerical and mathematical model, resulting in a nearly grid-independent solution. The simulation of an actual dam break shows the applicability of the scheme to nontrivial bathymetry and wave propagation on a dry bed.
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Published In
Journal of Hydraulic Engineering
Volume 130 • Issue 5 • May 2004
Pages: 412 - 421
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Oct 15, 2001
Accepted: Apr 9, 2003
Published online: Apr 15, 2004
Published in print: May 2004
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