This paper describes a new strongly-implicit line solution technique for the steady incompressible NavierStokes equations. The formulation leads to a second order accurate block tri-diagonal system of linear equations in term of primitive variables. It includes a new two stage pressure correction scheme which leads to extremely rapid convergence of all variables. The resulting computational model is structured so as to allow both the partiallyparabolized and the full NavierStokes equations to be solved with only trivial changes to the computer code, It has been tested for both internal and external flow problem and has proven to be both accurate and fast when applied to the solution of both the parabolized and the full form of the Navier -Stokes equations with dramatic reductions in computer time for both form of the equations.
BACKGROUND
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
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