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Higher-order solutions of square driven cavity flow using a variable- order multi-grid method. (English) Zbl 0757.76049

A new higher-order method is devised for the numerical simulation of square driven cavity flows. The spatial derivatives of the Navier-Stokes equations are discretized by means of the modified differential quadrature method. The resulting system of ordinary differential equations in time is then integrated by the classical fourth-order Runge- Kutta-Gill scheme. The elliptic (Poisson) equation is solved by means of a new variable-order multi-grid method. The numerical simulations of the square driven cavity flows are carried out with spatial order of accuracy up to 10th order.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N40 Method of lines for boundary value problems involving PDEs
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[1] Jones, J. Comp. Phys. 9 pp 496– (1972)
[2] and , BAIL III, Boole Press, 1984, pp. 291–296
[3] and , Lecture Notes in Physics 218, Springer-Verlag, Berlin, 1984, pp. 475–480.
[4] and , NASA TM-81339, 1982.
[5] Nishida, Mem. Fac. Eng. Des. Kyoto Inst. Technol. 36 pp 24– (1987)
[6] Wambecq, Computing 20 pp 333– (1978)
[7] Brandt, Math. Comp. 31 pp 333– (1977)
[8] Bellman, J. Comp. Phys. 10 pp 40– (1972)
[9] Hairer, Numerische Mathematik 35 pp 57– (1980)
[10] Ghia, J. Comp. Phys. 48 pp 387– (1982)
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