Nishida, Hidetoshi; Satofuka, Nobuyuki Higher-order solutions of square driven cavity flow using a variable- order multi-grid method. (English) Zbl 0757.76049 Int. J. Numer. Methods Eng. 34, No. 2, 637-653 (1992). 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. Cited in 15 Documents 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 Keywords:Poisson equation; modified differential quadrature method; fourth-order Runge-Kutta-Gill scheme PDFBibTeX XMLCite \textit{H. Nishida} and \textit{N. Satofuka}, Int. J. Numer. Methods Eng. 34, No. 2, 637--653 (1992; Zbl 0757.76049) Full Text: DOI References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.