Simultaneous Variable Solutions of the Incompressible Steady Navier-Stokes Equations in General Curvilinear Coordinate Systems

Abstract

A simultaneous variable solution technique for the incompressible, steady, two-dimensional Navier-Stokes equations in primitive formulation and general curvilinear orthogonal and nonorthogonal coordinate systems has been developed. The governing equations are discretized using finite difference approximations. The formulation is fully second order accurate and the well-known staggered grid of Welch and Harlow is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be accurate, robust and computationally efficient.