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A numerical algorithm for the Stokes problem based on an integral equation for the pressure via conformal mappings. (English) Zbl 0692.76019

Summary: We present an algorithm for solving numerically the Stokes problem in the plane. The known algorithms are all based on certain discretization schemes for the analytic equations. In contrast to this recent work our algorithm uses an explicit analytic solution of a certain ‘approximating problem’, which can easily be solved numerically up to machine accuracy. On the one hand this analytic formula is based on a complex representation of all solutions of the Stokes differential equations, and on the other hand it is based on the conformal mapping of the given domain on the unit disc. Therefore, a central prerequisite of our corresponding program is a program for computing this conformal mapping.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65N99 Numerical methods for partial differential equations, boundary value problems
30C30 Schwarz-Christoffel-type mappings

Software:

SCPACK
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Full Text: DOI EuDML

References:

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