A hybrid method for computing the flow of viscoelastic fluids. (English) Zbl 0753.76111

Summary: A hybrid method for computing the flow of viscoelastic and second-order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear. The method is applied to obtain the solutions to three problems of flow of Walter’s B’ fluid: (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.


76M20 Finite difference methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
76U05 General theory of rotating fluids
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[1] Beard, Proc. Camb. Phil. Soc. 60 pp 667– (1964)
[2] Rajeshwari, ZAMP 13 pp 43– (1962)
[3] Frater, ZAMP 21 pp 134– (1970)
[4] Davies, ZAMP 17 pp 189– (1960)
[5] Denn, Chem. Eng. Sci. 22 pp 395– (1967)
[6] Peddieson, AIChE J. 19 pp 377– (1973)
[7] Serth, J. Eng. Math. 8 pp 89– (1974)
[8] Ng, J. Comput. Phys. 39 pp 103– (1981)
[9] Bhatnagar, Rheol. Acta 17 pp 557– (1978)
[10] Rajagopal, Rheol. Acta 23 pp 213– (1984)
[11] Elliot, Phys. Fluids 14 pp 1086– (1971)
[12] Troy, Q. Appl. Math. 44 pp 753– (1987)
[13] Teipel, Rheol. Acta 25 pp 75– (1986)
[14] Rathna, ZAMM 42 pp 231– (1962)
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