A comparative study on the use of stabilized and flux-corrected transport finite element methods to solve the shallow water equations

Santos T. L., Coutinho A. L. G. A. - CILAMCE 2019 – XL Ibero-Latin American Congress on Computational Methods in Engineering. 2019.

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 integration 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.

Palavras-chave

stabilized finite element, SUPG, shock capturing, flux-corrected transport, shallow water