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1 International Journal of Applied Mechanics and Engineering

1 2011

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Finite difference schemes and the method of lines for solving incompressible viscous flow problems

Kosma Z., Motyl P.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 1

15-35

For the determination of viscous incompressible flows a pure stream-function formulation for the fourth-order equation, the artificial compressibility method, and velocity correction method are employed. Test calculations are performed for various flows inside square, triangular, semicircular and cubic cavities with one uniform wall, the backward-facing step, double bent channels, the flow around an aerofoil at large angle of attack and for flows over models of buildings. Some complex geometrical configurations can be decomposed into a set of simpler subdomains. A practical methodology for the computation of the Navier-Stokes equations in arbitrarily complex geometries is also considered. The simplest approach for specifying boundary conditions near curved or irregular boundaries is to transfer all the variables from the boundaries to the nearest grid knots.