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A Numerical Method for Nonstationary Stokes Flow

In: Advances in Mathematical Fluid Mechanics

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  • Werner Varnhorn

    (Fachbereich Mathematik, Universität Kassel)

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.

Suggested Citation

  • Werner Varnhorn, 2010. "A Numerical Method for Nonstationary Stokes Flow," Springer Books, in: Rolf Rannacher & Adélia Sequeira (ed.), Advances in Mathematical Fluid Mechanics, pages 589-611, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04068-9_33
    DOI: 10.1007/978-3-642-04068-9_33
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