Numerical Simulation for 2D Sedimentation Model by an Upwind Discontinuous Galerkin Procedure

摘要

We reformulate the mathematical model for the 2D sedimentation in an estuary as a coupled nonlinear differential system. Combining the mass-conservation character of the discontinuous Galerkin method and the jump-capturing property of Lesaint-Raviart upwind technique, we design an upwind discontinuous Galerkin finite element method, which obeys the local mass conservation and possesses good stability. Our theoretical analysis shows that there exists a unique solution to the numerical procedure and the discrete solution permits O(h(k) + Delta t) convergence rate. Numerical experiments are conducted to verify our theoretical findings. This may provide a theoretical principle for better understanding of the mechanism and morphological characters of sedimentation at estuaries.