Year: 2013
Author: Werner Varnhorn, Florian Zanger
Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 2 : pp. 151–171
Abstract
We present an approximation method for the non-stationary nonlinear incompressible Navier-Stokes equations in a cylindrical domain (0,T)×G,where G⊂R^3 is a smoothly bounded domain. Ourmethod is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and representation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v·∇v we obtain globally (in time) uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v26.n2.5
Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 2 : pp. 151–171
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Navier-Stokes equations