A COMPARATIVE STUDY ON THE USE OF STABILIZED AND FLUX-CORRECTED TRANSPORT FINITE ELEMENT METHODS TO SOLVE THE SHALLOW WATER EQUATIONS
Palavras-chave:
Stabilized finite element, SUPG, Shock capturing, Flux-corrected transport, Shallow waterResumo
A study is carried out to assess the use of stabilized and flux-corrected transport (FCT) finite
element approaches to solve the shallow water equations. The adopted stabilized formulation employs a
Streamline Upwind Petrov-Galerkin term supplemented by a shock-capturing operator. In the examined
FCT technique, the low-order equation considers an artificial viscosity term based on a Rusanov-like
scalar dissipation. Anti-diffusive fluxes are linearized around the low-order solution and limited with
the Zalesak’s algorithm. Both approaches use semi-discrete finite elements with implicit time integra-
tion over time steps constrained by a CFL condition. Numerical results are presented for standard test
problems available in the literature, and the accuracy and stability of the solutions are discussed.
