Summary
A new finite-difference scheme for the incompressible Navier-Stokes equations in two space dimensions is formulated. This scheme uses the velocity vector and the pressure gradients as dependent variables. A Multi-Grid scheme for the system of equations is proposed. The algebraic convergence rate of the new (PGA-MG) scheme is compared to the convergence of the (DGS-MG) scheme of Brandt and Dinar [1]. As test problems we use either a smooth test case, the flow in a driven cavity or the flow in a separator model.These problems represent flows with decreasing order of smoothness. It was found that the new PGA-MG scheme has a good convergence rate even for those Reynolds numbers for which the DGS-MG scheme is unstable.
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References
Brandt, A. and Dinar, N.: Multigrid solution to elliptic flow problems, in Numerical methods in PDE, S.V. Parter ed. pp. 53–147, Academic Press (1979).
Thunell, T and Fuchs, L.: Numerical solution of the Navier-Stokes equations by Multi-Grid techniques, in Numerical methods in laminar and turbulent flow, C. Taylor and A.B. Schrefler eds. pp. 141–152, Pineridge Press (1981).
Fuchs, L. and Zhao, H-S.: Solution of three-dimensional viscous incompressible flows by a multi-grid method Numerical Methods in Fluids (1984) to appear.
Fuchs, L.: New relaxation methods for incompressible flow problems, in Numerical methods in laminar and turbulent flow, C. Taylor, J.A. Johnson and W.R. Smith eds. pp. 606–616, Pineridge Press (1983).
Fuchs, L.: A fast numerical method for the solution of boundary value problems, TRITA-GAD-4, ISSN 0281–7721 (1980).
Fuchs, L.: Multi-Grid solution of the Navier-Stokes equations on nonuniform grids, in NASA CP-2202, pp. 83–100 (1981).
Harlow, F.H. and Welch, J.E.: Numerical calculation of time-dependent incompressible flow, Physics of Fluids, Vol. 8, pp. 2182–2187 (1965).
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© 1984 Springer Fachmedien Wiesbaden
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Fuchs, L. (1984). Multi-Grid Schemes for Incompressible Flows. In: Hackbusch, W. (eds) Efficient Solutions of Elliptic Systems. Notes on Numerical Fluid Mechanics, vol 10. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14169-3_4
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DOI: https://doi.org/10.1007/978-3-663-14169-3_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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Online ISBN: 978-3-663-14169-3
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