Author(s): Kesserwani Georges; Ghostine Rabih; Vazquez Jose; Mose Robert; Ghenaim Abdellah
Linked Author(s): Georges Kesserwani
Keywords: St. Venant; Source terms; RKDG2; Boundary conditions; Discontinuous flows
Abstract: The present work addresses the numerical prediction of discontinuous shallow water flows with irregular topography. The unsteady flow of water in a one-dimensional approach is described by the set of St. Venant’s hyperbolic equations which incorporates source terms in the non-idealized case. Therefore, a second order version —in space and time— of the Runge-Kutta discontinuous Galerkin scheme (RKDG2) was detailed and applied to solve the shallow water equations in conservative form. Further, an adequate boundary condition handling by the theory of characteristics was overviewed to be adapted to the external points of the mesh, as well to some point of local invalidity for the St. Venant model. To validate the RKDG2 scheme, three different steady discontinuous flow problems with analytical solutions; as well as to a fourth practical problem involving internal boundary conditions, were considered and computed by means of the RKDG2 scheme. Its results were illustrated near the results of a widely used finite volume second order TVD scheme —in space and time—, together with the analytical solutions. Strong numerical evidence shows that the proposed model’s implementation is accurate, robust, conservative and highly stable in capturing strong gradients and discontinuities in transcritical flows, and is a reliable model for one-dimensional practical applications in hydraulics engineering.
Year: 2007