A Numerical Method for Nonstationary Stokes Flow

Werner Varnhorn ()
Additional contact information
Werner Varnhorn: Fachbereich Mathematik, Universität Kassel

A chapter in Advances in Mathematical Fluid Mechanics, 2010, pp 589-611 from Springer

Abstract: Abstract We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in a cylindrical domain (0, T ) × G where G ⊂ R3 is smoothly bounded. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces H m (G) (m = 0, 1, 2) uniformly for t ∈ [0, T], provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations' systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. The main purpose of this paper is to combine these steps to an efficient numerical algorithm for non-stationary Stokes flow and illustrate its accuracy via different simulations of a model problem.

Keywords: Stokes equations; Time stepping; Stokes resolvent potentials; Boundary element methods (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04068-9_33

Ordering information: This item can be ordered from
http://www.springer.com/9783642040689

DOI: 10.1007/978-3-642-04068-9_33

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().