The method of lines for the computation of incompressible viscous flows

A common approach to finding numerical solutions of the time-dependent incompressible Navier-Stokes equations is considered within the method of lines framework [1]. For the determination of viscous incompressible flows the stream-function formulation for the fourth-order equation [2, 3], an artificial compressibility method [4], and a modified velocity correction method [5] are designed. Some improved and extended results of numerical simulations obtained by the author in the previous works are presented. Test calculations have been done for various flows inside square, triangular and semicircular cavities with one moving wall, the backward-facing step, double bent channels and for the flow around an aerofoil at large angle of attack. An alternative and practical methodology for resolving the Navier-Stokes equations in arbitrarily complex geometries using Cartesian meshes is proposed. Some of complex geometrical configurations can be decomposed into a set of subdomains. 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. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)