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.

► We present a continuous positive definite CBS-FE model for the shallow water equations. ► Model incorporates flux corrected techniques and low order upwind method. ► Main experiments are the propagation of water fronts over dry beds for floods and dam breaking problems. ► Computational cost is close to some current FEM_FCT models.