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A fully implicit direct Newton's method for the steady-state Navier–Stokes equations

✍ Scribed by Dana A. Knoll; Paul R. McHugh

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
740 KB
Volume
17
Category
Article
ISSN
0271-2091

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✦ Synopsis

Newton's method and banded Gaussian elimination can be a CPU efficient method for steady-state solutions to two-dimensional Navier-Stokes equations. In this paper we look at techniques that increase the radius of convergence of Newton's method, reduce the number of times the Jacobian must be factored, and simplify evaluation of the Jacobian. The driven cavity and natural convection problems are used as test problems, and finite volume discretization is employed.

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The present paper provides an improved alternating direction implicit (ADI) technique as well as a highorder-accurate spline AD1 method for the numerical solution of steady two-dimensional incompressible viscous flow problems. The vorticity-stream function Navier-Stokes equations are considered in a