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A fully implicit direct Newton’s method for the steady-state Navier- Stokes equations. (English) Zbl 0784.76068
Summary: 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.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
76R10 Free convection
65F10 Iterative numerical methods for linear systems
Software:
YSMP
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References:
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