Solution of the Steady State Incompressible Navier-Stokes Equations in Curvilinear Nonorthogonal Coordinates

摘要

An implicit Navier-Stokes solver was developed using the approximate factorization method of Beam and Warming (1978 to 1979) to solve two dimensional incompressible laminar steady internal flows using the primitive variables formulation of the Navier-Stokes equations. The Chorin (1967) artificial compressibility equation is employed to evaluate the pressure. Spherical coordinates are used to allow the numerical model to cope with the largest possible number of wall geometries. Methods for the introduction of the artificial dissipation terms needed to obtain wiggles-free results when using a centered space discretization are proposed. Formulations for a time step variable in space were tested to improve the convergence rate. Flows in channels with streamlined walls, backward facing steps, and channels with obstacles were computed.