𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finite element solution for the transcritical shallow-water equations

✍ Scribed by Nicole Goutal; J. C. Nedelec

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
708 KB
Volume
11
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Communicated by J. C. Nedelec

A new solution of the two-dimensional shallow-water equations, using a finite element method is described. The formulation is based on the velocity and height variables and follows two step. In the first step, the convective terms are solved by a characteristic method and in the second step the propagative and diffusion terms are taken into account. The close relation between the latter operator and a Stokes penalized problem is shown; an algorithm of Uzawa type is then used for its solution. Acceleration convergence is obtained by preconditioning, and new methods are presented, the quality of the convergence being shown on application to some sample tests. The overall method has revealed quite efficient and application to industrial cases is already planned.

πŸ“œ SIMILAR VOLUMES

Compatibility between finite volumes and
Compatibility between finite volumes and finite elements using solutions of shallow water equations for substance transport
✍ Leo Postma; Jean-Michel Hervouet πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 373 KB

## Abstract This paper formulates a finite volume analogue of a finite element schematization of three‐dimensional shallow water equations. The resulting finite volume schematization, when applied to the continuity equation, exactly reproduces the set of matrix equations that is obtained by the app

A split-characteristic based finite elem
A split-characteristic based finite element model for the shallow water equations
✍ O. C. Zienkiewicz; P. Ortiz πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 895 KB

A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator-splitting procedure for which a characteristic-based rational form of including balancing dissipation terms is achieved. In the semi-explicit form the method circumvents