Non-oscillatory continuous FEM for transport and shallow water flows
The paper presents a sign-preserving continuous finite element model (FEM) for coupled transport equations, and in particular for the depth-integrated shallow water equations. The model incorporates an enhanced flux corrected transport method (FCT) with a high order solution given by a generalization of the characteristic based split finite element method (CBS), and a predictor positive algorithm founded in a finite element upwind methodology. Numerical experiments explore the efficacy of the procedure, with emphasis in the simulation of flows with evolutionary boundaries determined by null values of any flow property, and in severe conditions of propagation such as dam-breaking waves.
shallow water equations flux correction continuous galerkin finite elements positive definite algorithm