On numerical stabilization in the solution of Saint-Venant equations using the finite element method

10Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

Abstract

Solving the Saint-Venant equations by using numerical schemes like finite difference and finite element methods leads to some unwanted oscillations in the water surface elevation. The reason for these oscillations lies in the method used for the approximation of the nonlinear terms. One of the ways of smoothing these oscillations is by adding artificial viscosity into the scheme. In this paper, by using a suitable discretization, we first solve the one-dimensional Saint-Venant equations by a finite element method and eliminate the unwanted oscillations without using an artificial viscosity. Second, our main discussion is concentrated on numerical stabilization of the solution in detail. In fact, we first convert the systems resulting from the discretization to systems relating to just water surface elevation. Then, by using M-matrix properties, the stability of the solution is shown. Finally, two numerical examples of critical and subcritical flows are given to support our results. © 2011 Elsevier Ltd. All rights reserved.

Cite

CITATION STYLE

APA

Zarmehi, F., Tavakoli, A., & Rahimpour, M. (2011). On numerical stabilization in the solution of Saint-Venant equations using the finite element method. Computers and Mathematics with Applications, 62(4), 1957–1968. https://doi.org/10.1016/j.camwa.2011.06.039

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free