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, twodimensional 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.Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 06/16/2015 Terms of Use: http://asme.org/terms (ii) Laminar Flow in a Channel With a Constriction. The second test problem is the laminar flow in a channel with a constriction. The constriction geometry is shown in Fig. 9(a) and is defined by a Gaussian distribution. The maximum of the distribution, appearing dXx = 2, restricts the height of the Journal of Fluids Engineering SEPTEMBER 1992, Vol. 114 / 303 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 06/16/2015 Terms of Use: http://asme.org/terms

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

“…Cheng [3] investigated steady viscous flow through a channel with symmetric cosinusoidal constrictions on both the walls at the same location. Vradis et al [4] studied steady incompressible viscous flow in a channel with local constriction having the shape of a Gaussian distribution. Mahapatra et al [5] studied flow separation in a constricted channel without assuming flow symmetry about the channel centreline.…”