TY - JOUR
T1 - On Approximation and Computation of Navier-Stokes Flow
AU - Varnhorn , Werner
AU - Zanger , Florian
JO - Journal of Partial Differential Equations
VL - 2
SP - 151
EP - 171
PY - 2013
DA - 2013/06
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n2.5
UR - https://global-sci.org/intro/article_detail/jpde/5159.html
KW - Navier-Stokes equations
KW - regularization
KW - time delay
KW - finite differences
KW - Stokes resolvent
KW - hydrodynamical potential theory
KW - boundary element methods
KW - numerical simulation
AB - <p>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.</p>