×

zbMATH — the first resource for mathematics

Application of generalized differential quadrature rule in Blasius and Onsager equations. (English) Zbl 0996.76072
Summary: The generalized differential quadrature rule (GDQR) is applied to third-order nonlinear differential equations of Blasius type and to sixth-order linear Onsager differential equations. High \((\geq\text{3rd})\)-order differential equations in fluid mechanics are dealt with without using \(\delta\)-point techniques. The half-space domain is simplified in a practical way, and accurate results are obtained for both kinds of problems. The applicability of GDQR in high-order differential equations is manifested further through this work.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76U05 General theory of rotating fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bellman, Journal of Mathematical Analysis Application 34 pp 235– (1971) · Zbl 0236.65020 · doi:10.1016/0022-247X(71)90110-7
[2] Chen, International Journal for Numerical Methods in Engineering 40 pp 1941– (1997) · Zbl 0886.73078 · doi:10.1002/(SICI)1097-0207(19970615)40:11<1941::AID-NME145>3.0.CO;2-V
[3] Wang, International Journal for Numerical Methods in Engineering 40 pp 759– (1997) · Zbl 0888.73078 · doi:10.1002/(SICI)1097-0207(19970228)40:4<759::AID-NME87>3.0.CO;2-9
[4] Bellomo, Mathematical Computation Modelling 26 pp 13– (1997) · Zbl 0898.65074 · doi:10.1016/S0895-7177(97)00142-8
[5] A Generalization of the differential quadrature method. The Abstract Book for ICTAM 2000, The 20th International Congress of Theoretical and Applied Mechanics, Chicago, 27 August-1 September 2000, p. 119.
[6] Wu, Journal of Sound and Vibration 233 pp 195– (2000) · Zbl 1237.65018 · doi:10.1006/jsvi.1999.2815
[7] Wu, Computational Mechanics 24 pp 197– (1999) · Zbl 0976.74557 · doi:10.1007/s004660050452
[8] A generalized differential quadrature rule for analysis of thin cylindrical shells. In Computational Mechanics for the Next Millennium 1. (Proceedings of Fourth Asia-Pacific Conference on Computational Mechanics, 1999, (eds)). Elsevier: Amsterdam, p. 223-228.
[9] Wu, International Journal of Pressure Vessels Piping 77 pp 149– (2000) · doi:10.1016/S0308-0161(00)00006-5
[10] Wu, International Journal for Numerical Methods in Engineering 50 pp 1907– (2001) · Zbl 0999.74120 · doi:10.1002/nme.102
[11] Wu, Communications in Numerical Methods in Engineering 16 pp 777– (2000) · Zbl 0969.65070 · doi:10.1002/1099-0887(200011)16:11<777::AID-CNM375>3.0.CO;2-6
[12] Wu, Communications in Numerical Methods in Engineering
[13] Liu, Mathematical and Computer Modelling
[14] Shu, International Journal for Numerical Methods in Fluids 15 pp 791– (1992) · Zbl 0762.76085 · doi:10.1002/fld.1650150704
[15] Striz, International Journal of Non-Linear Mechanics 29 pp 665– (1994) · Zbl 0825.76615 · doi:10.1016/0020-7462(94)90063-9
[16] Laminar boundary layers. Oxford University Press: Oxford, 1966.
[17] Wood, Journal of Fluid Mechanics 101 pp 1– (1980) · Zbl 0462.76071 · doi:10.1017/S0022112080001504
[18] Viecelli, Journal of Computational Physics 50 pp 162– (1983) · Zbl 0521.76107 · doi:10.1016/0021-9991(83)90046-3
[19] Bert, Applied Mechanics Reviews 49 pp 1– (1996) · doi:10.1115/1.3101882
[20] A theoretically derived transfer function for oil recovery from fractured reservoirs by waterflooding. SPE 27745, Proceedings of the 1994 Improved Oil Recovery Symposium, Tulsa, OK, 87-98, 1994.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.