Bringing out Fluids Experiments from Laboratory to In Silico – A Journey of Hundred Years

Manickam Siva Kumar, Pichai Philominathan

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DOI: 10.4236/ajcm.2011.14033                

Abstract

By making use of the developments in the fields of numerical methods, computational technology and fluid dynamics models, computational fluid dynamics (CFD) progress forward to play an active role today in various industrial, academic and research activities. In many cases, CFD simulations replace expensive and time consuming laboratory experiments successfully by allowing engineers and scientists to capture pressure, velocity and force distributions. Researchers are now able to test various theoretical conditions unavailable in the laboratory and CFD studies help them to get deeper insights on existing theories. The century-old history started just to solve some stress analysis problems numerically and today CFD methodology is being applied not only in fluid dynamics also in chemical engineering, mineral processing, fire engineering, sports, medical imaging and even in acoustics. This paper reviews the growth of CFD as a discipline and discusses its contemporary methodology.

Keywords

Fluid Dynamics, Computation Fluid Dynamics, Numerical Methods And Algorithms

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Courant, K. Friedrichs and H. Lewy, “Uber die Partiel- lendifferenzgleichungen der Mathematischen Physik,” Ma- thematische Annalen, Vol. 100, No. 1, 1928, pp. 32-74. doi:10.1007/BF01448839
[2]	L. F. Richardson, “The Approximate Arithmetical Solu- tion by Finite Differences of Physical Problems Involving Differential Equations with an Application to the Stresses in Masonry Dam,” Philosophical Transactions of the Royal Society of London. Series A, Vol. 210, No. 459-470, 1910, pp. 307-357.
[3]	Z. Kopal, “Tables of Supersonic Flow around Cones,” Department of Electrical Engineering Cambridge, Center of Analysis, Massachusetts Institute of Technology, 1947.
[4]	T. J. Chung, “Computational Fluid Dynamics,” Cam- bridge University Press, Cambridge, 2002. doi:10.1017/CBO9780511606205
[5]	A. Thom, “The Flow Past Circular Cylinders at Low Speeds,” Proceedings of the Royal Society of London. Series A, Vol. 141, No. 845, 1933, pp. 651-666. doi:10.1098/rspa.1933.0146
[6]	M. Kawaguti, “Numerical Solution of the NS Equations for the Flow around a Circular Cylinder at Reynolds Num- ber 40,” Journal of Physical Society of Japan, Vol. 8, No. , 1953, pp. 747-757. doi:10.1143/JPSJ.8.747
[7]	S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” Hemisphere Publishing Corp., Washington DC, 1980.
[8]	R. P. Loui, “Top 100 Hits,” 2008. (cited 2 October 2011). http://www.cse.wustl.edu/~loui/goocites.html
[9]	D. Gottlieb and S. A. Orszag, “Numerical Analysis of Spec- tral Methods: Theory and Applications Pennsylvania,” SIAM, Philadelphia, 1993.
[10]	J. G. Zhou, “Lattice Boltzmann Methods for Shallow Water Flows Newyork,” Springer, Berlin, 2004.
[11]	J. H. Ferziger and M. Peric, “Computational Methods for Fluid Dynamics,” Springer, Berlin, 2002. doi:10.1007/978-3-642-56026-2
[12]	C. Sells, “Plane Subcritical Flow Past a Lifting Aerofoil,” Proceedings of the Royal Society of London. Series A, Vol. 308, No. 1494, 1968, pp. 377-401.
[13]	T. J. Baker, “Mesh Generation: Art or Science?” Progress in Aerospace Sciences, Vol. 41, No. 1, 2005, pp. 29-63. doi:10.1016/j.paerosci.2005.02.002
[14]	A. Denayer, “Automatic Generation of Finite Element Meshes,” Computers & Structures, Vol. 9, No. 4, 1978, pp. 359-364.
[15]	Wordenweber, “Volume Triangulation,” CAD Group Do- cument No. 110, University of Cambridge, Cambridge, 1980.
[16]	W. C. Thacker, A. Gonzalez and G. E. Putland, “A Me- thod for Automating the Construction of Irregular Com- putational Grids for Storm Surge Forecaste Models,” Journal of Computational Physics, Vol. 37, No. 3, 1980, pp. 371-387. doi:10.1016/0021-9991(80)90043-1
[17]	S. F. Yeung and M. B. Hsu, “A Mesh Generation Method Based on Set Theory,” Computers & Structures, Vol. 3, No. 5, 1973, pp. 1063-1077. doi:10.1016/0045-7949(73)90038-2
[18]	W. Barfield, “Numerical Method for Generating Ortho- gonal Curvilinear Meshes,” Journal of Computational Phy- sics, Vol. 5, No. 1, 1970, pp. 23-33. doi:10.1016/0021-9991(70)90050-1
[19]	A. Bykat, “Design of a Recursive, Shape Controlling Mesh Generator,” International Journal for Numerical Methods in Engineering, Vol. 19, No. 9, 1983, pp. 1375-390. doi:10.1002/nme.1620190907
[20]	J. E. Thompson, Z. U. A. Warsi and C. W. Mastin, “Nu- merical Grid Generation-Foundations and Applications,” Elsevier, New York, 1985.
[21]	A. S. Arcilla, J. H?user, P. R. Eiseman and J. E. Thompson, “Numerical Grid Generation in Computational Fluid Dy- namics and Related Fields,” North-Holland, Amsterdam, 1991.
[22]	V. D. Liseikin, “Grid Generation Ethods,” Springer-Ver- lag, Berlin, 1999.
[23]	S. V. Patankar and D. B. Spalding, “A Calculation Proce- dure for Heat, Mass and Momentum Transfer in Three- Dimensional Parabolic Flows,” International Journal of Heat and Mass Transfer, Vol. 15, No. 10, 1972, pp. 1787-1805. doi:10.1016/0017-9310(72)90054-3
[24]	J. P.V. Doormaal and G. D. Raithby, “Enhancements of the SIMPLE Method for Predicting Incompressible Flow Problems,” Numerical Heat Transfer, Vol. 7, No. 2, 1984, pp. 147-163.
[25]	D. W. Peaceman and H. H. J. Rachford, “The Numerical Solution of Parabolic and Elliptic Differential Equations,” Journal of Society for Industrial and Applied Mathemat- ics, Vol. 3, No. 1, 1955, pp. 28-41. doi:10.1137/0103003
[26]	H. L. Stone, “Iterative Solution of Implicit Approxima- tions of Multidimensional Partial Differential Equations,” SIAM Journal on Numerical Analysis, Vol. 5, No. 3, 1968, pp. 530-558. doi:10.1137/0705044
[27]	R. I. Issa, “Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting,” Journal of Com- putational Physics, Vol. 62, No. 1, 1986, pp. 40-65. doi:10.1016/0021-9991(86)90099-9
[28]	Y. Saad and M. H. Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific Computing, Vol. 7, No. 3, 1986, pp. 856-869. doi:10.1137/0907058
[29]	W. Hackbusch, “Multigrid Methods and Applications- omputational Mathematics,” Springer-Verlag, Berlin, 1985.
[30]	J. Argyris and P. Patton, “Computer Oriented Research in a Universitymilieu,” Applied Mechanics Reviews, Vol. 19, No. 12, 1966, pp. 1029-1039.
[31]	L. Richardson, “Weather Prediction by Numerical Proc- ess,” Cambridge University Press, Cambridge, 1922.
[32]	J. J. Monaghan, “An Introduction to SPH,” Computer Phy- sics Communications, Vol. 48, No. 1, 1988, pp. 88-96. doi:10.1016/0010-4655(88)90026-4
[33]	B. Cabral and L. C. Leedom, “Imaging Vector Fields Us- ing Line Integral Convolution,” Proceeding of the 20th Annual Conference on Computer Graphics, Anaheim, 1993, pp. 263-270.
[34]	R. S. Laramee, H. Hauser, H. Doleisch, B. Vrolijk, F. H. Post and D. Weiskopf, “The State of the Art in Flow Visualization: Dense and Texture-Based Techniques,” Com- puter Graphics Forum, Vol. 23, No. 2, 2004, pp. 143-161.
[35]	F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee and H. Doleisch, “The State of the Art in Flow Visualization: Feature Extraction and Tracking,” Computer Graphics Forum, Vol. 22, No. 4, 2003, pp. 775-792. doi:10.1111/j.1467-8659.2003.00723.x
[36]	F. H. Harlow and J. E. Fromm, “Computer Experiments in Fluid Dynamics,” Scientific American, Vol. 213, No. 3, 1965, pp. 104-110. doi:10.1038/scientificamerican0365-104
[37]	P. J. Roache, “Computational Fluid Dynamics,” Hermosa Publications, Albuquerque, 1972.
[38]	M. W. Evans and F. H. Harlow, “The Particle-in-Cell Method for Hydrodynamic Calculations,” Scientific La- boratory Report, Los Alamos, 1957.
[39]	J. L. Hess, “Review of the Source Panel Technique for ?ow Computation,” In: R. P. Shaw, J. Periaux, A. Chaudouet, J. Wu, L. Morino and C. A. Brebbia, Eds, Proceedings of 4th International Symposium on Innovative Numerical Methods in Engineering, Atlanta, Springer-Verlag, 1986, pp. 197-210.
[40]	J. L. Hess, “Panel Methods in Computational Fluid Dy- namics,” Annual Review of Fluid Mechanics, Vol. 22, No. 1, 1990, pp. 255-74. doi:10.1146/annurev.fl.22.010190.001351
[41]	Y. Sun, Z. J. Wang and Y. Liu, “Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids: Extension to Viscous Flow,” Journal of Computational Physics, Vol. 215, No. 1, 2006, pp. 41-58. doi:10.1016/j.jcp.2005.10.019
[42]	H. T. Huynh, “A Flux Reconstruction Approach to High- Order Schemes Including Discontinuous Galerkin Meth- ods,” Computational Fluid Dynamics Meeting, 2007, 4079.
[43]	M. Siva Kumar and P. Philominathan, “Computational Fluid Dynamics Modeling Studies on Bacterial Flagellar Motion,” International Journal of Fluid Machinery and Systems, Vol. 4, No. 3, 2011, pp. 341-348.