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Aspectos matemáticos de algunos métodos numéricos en mecánica de fluidos: el problema incompresible de Navier-Stokes

 

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Opened Access Aspectos matemáticos de algunos métodos numéricos en mecánica de fluidos: el problema incompresible de Navier-Stokes
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Author: Fernández Cara, Enrique
Marín Beltrán, Mercedes
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 1987
Published in: Revista internacional de métodos numéricos para cálculo y diseño en ingeniería, 3 (2), 129-152.
Document type: Article
Abstract: El objetivo de este estudio ha sido la obtención de propiedades de convergencia y estabilidad para dos esquemas numéricos que permiten resolver las ecuaciones incompresibles de Navier-Stokes. Dichos esquemas han sido obtenidos modificando ligerament...
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The goal of this paper is to describe some stability and convergence properties for two numerical schemes which can be used to solve the incompressible time-dependent Navier-Stokes equations. The schemes were derived by modifying slightly others, due to R. Glowinski, for which convergence had not still been proven. At a first stage, alternating direction time-discretization methods of Peaceman-Rachford and Strang types have been introduced. This reduces the task to the solution of a sequence of (stationary) elliptic subproblems, some of them linear (quasi-Stokes problems) and some quasilinear. Then, these are solved using FEMs for the nonlinear sub-problems, it is appropiate to introduce a least-squares reformulation). Under certain specific stability conditions, we establish a convergence result for the computed solutions. This justifies rigorously the fact that Glowinski's methods have provided excellent numerical results.
Cite: Fernández Cara, E. y Marín Beltrán, M. (1987). Aspectos matemáticos de algunos métodos numéricos en mecánica de fluidos: el problema incompresible de Navier-Stokes. Revista internacional de métodos numéricos para cálculo y diseño en ingeniería, 3 (2), 129-152.
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URI: http://hdl.handle.net/11441/48782

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