A fast poisson solver for the finite difference solution of the incompressible navier-stokes equations

In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier--Stokes equations. To achieve our goal, new algorithms for diagonalizing a semi...

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Bibliographic Details
Published in:SIAM journal on scientific computing 1998-09, Vol.19 (5), p.1606-1624
Main Authors: GOLUB, G. H, LAN CHIEH HUANG, SIMON, H, TANG, W.-P
Format: Article
Language:English
Subjects:
Approximation
Classical and quantum physics: mechanics and fields
Classical mechanics of continuous media: general mathematical aspects
Computational mathematics
Computer science
Exact sciences and technology
Fluid mechanics: general mathematical aspects
Laboratories
Mathematics
Navier-Stokes equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Sciences and techniques of general use
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Summary:In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier--Stokes equations. To achieve our goal, new algorithms for diagonalizing a semidefinite pair are developed. The fast solver can also be extended to the three-dimensional case. The motivation and related issues in using this half-staggered grid are also discussed.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595285299