The numerical solution of the two-dimensional unsteady Navier-Stokes equations using fourth-order difference method. (English) Zbl 0744.76084

Summary: In this paper, high-order finite difference methods of \(O(k^ 2+kh^ 2+h^ 4)\) using 9-spatial grid points for integrating the system of two- dimensional nonlinear parabolic partial differential equations subject to Dirichlet boundary conditions are given. The method having two variables is tested on 2-D unsteady Navier-Stokes equations. Numerical examples given here show that the methods developed here retain their order and accuracy.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N06 Finite difference methods for boundary value problems involving PDEs
Full Text: DOI


[1] DOI: 10.1137/0724081 · Zbl 0637.76022 · doi:10.1137/0724081
[2] DOI: 10.1007/BF01535362 · Zbl 0255.76027 · doi:10.1007/BF01535362
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[7] DOI: 10.1016/0045-7930(73)90027-3 · Zbl 0328.76020 · doi:10.1016/0045-7930(73)90027-3
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