×

Modeling low Reynolds number incompressible flows using SPH. (English) Zbl 0889.76066

Summary: The method of smoothed particle hydrodynamics (SPH) is extended to model incompressible flows at low Reynolds number. Treatment of viscosity, state equation, kernel interpolation, and boundary conditions are described. Simulations using the method show close agreement with series solutions for Couette and Poiseuille flows. Furthermore, comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D99 Incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lucy, L. B., A numerical approach to the testing of the fission hypothesis, Astron. J., 83, 1013 (1977)
[2] Gingold, R. A.; Monaghan, J. J., Smoothed particle hydrodynamics: Theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., 181, 375 (1977) · Zbl 0421.76032
[3] Monaghan, J. J., Simulating free surface flows with SPH, J. Comput. Phys., 110, 399 (1994) · Zbl 0794.76073
[4] Artymowicz, P.; Lubow, S. H., Dynamics of binary-disk interaction. 1. Resonances and disk gap sizes, Astrophys. J., 421, 651 (1994)
[5] Takeda, H.; Miyama, S. M.; Sekiya, M., Numerical simulation of viscous flow by Smoothed Particle Hydrodynamics, Prog. Theor. Phys., 92, 939 (1994)
[6] W. Benz, 1989, Smooth particle hydrodynamics: A review, NATO Workshop, Les Arcs, France, 1989; W. Benz, 1989, Smooth particle hydrodynamics: A review, NATO Workshop, Les Arcs, France, 1989
[7] Monaghan, J. J., Smoothed Particle Hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543 (1992)
[8] Courant, R.; Friedrichs, K.; Lewy, H., Über die partiellen differenzengleichungen der mathematischen physik, Math. Ann., 100, 32 (1928) · JFM 54.0486.01
[9] Chorin, A. J., A numerical method for solving incompressible flow problems, J. Comput. Phys., 2, 12 (1967) · Zbl 0149.44802
[10] Turkel, E., Preconditioned methods for solving the incompressible and low-speed compressible equations, J. Comput. Phys., 72, 277 (1987) · Zbl 0633.76069
[11] Tamamidis, P.; Zhang, G.; Assanis, D. N., Comparison of pressure-based and artificial compressibility methods for solving three-dimensional steady incompressible viscous flows, J. Comput. Phys., 124, 1 (1996) · Zbl 0848.76054
[12] J. J. Monaghan, 1995, Simulating gravity currents with SPH lock gates, Applied Mathematics Reports and Preprints, 95/5, Monash University; J. J. Monaghan, 1995, Simulating gravity currents with SPH lock gates, Applied Mathematics Reports and Preprints, 95/5, Monash University
[13] Batchelor, G. K., An Introduction to Fluid Dynamics (1967), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0152.44402
[14] J. P. Morris, 1994, A study of the stability properties of SPH, Applied Mathematics Reports and Preprints, 94/22, Monash University, Melbourne, Australia; J. P. Morris, 1994, A study of the stability properties of SPH, Applied Mathematics Reports and Preprints, 94/22, Monash University, Melbourne, Australia
[15] Balsara, D. S., Von-Neumann stability analysis of Smoothed Particle Hydrodynamics: Suggestions for optimal algorithms, J. Comput. Phys., 121, 357 (1995) · Zbl 0835.76070
[16] Swegle, J. W.; Hicks, D. L.; Attaway, S. W., Smoothed Particle Hydrodynamics stability analysis, J. Comput. Phys., 116, 123 (1995) · Zbl 0818.76071
[17] Morris, J. P., Stability Properties of SPH, Publ. Astron. Soc. Aust., 13, 97 (1996)
[18] Monaghan, J. J., On the problem of penetration in particle methods, J. Comput. Phys., 82, 1 (1989) · Zbl 0665.76124
[19] J. J. Monaghan, 1995, Improved modelling of boundaries, Applied Mathematics Reports and Preprints, 95/30, Monash University, Melbourne, Australia; J. J. Monaghan, 1995, Improved modelling of boundaries, Applied Mathematics Reports and Preprints, 95/30, Monash University, Melbourne, Australia
[20] J. J. Monaghan, 1995, Simulating gravity currents with SPH: III boundary forces, Applied Mathematics Reports and Preprints, 95/11, Monash University, Melbourne, Australia; J. J. Monaghan, 1995, Simulating gravity currents with SPH: III boundary forces, Applied Mathematics Reports and Preprints, 95/11, Monash University, Melbourne, Australia
[21] Libersky, L. D.; Petschek, A. G.; Carney, T. C.; Hipp, J. R.; Allahdadi, F. A., High strain Lagrangian hydrodynamics, J. Comput. Phys., 109, 67 (1993) · Zbl 0791.76065
[22] Maddison, S. T.; Murray, J. R.; Monaghan, J. J., SPH simulations of accretion disks and narrow rings, Publ. Astron. Soc. Aust., 13, 66 (1996)
[23] Flebbe, O.; Münzel, S.; Herold, H.; Riffert, H.; Ruder, H., Smoothed Particle Hydrodynamics: Physical viscosity and the stimulation of accretion disks, Astrophys. J., 431, 754 (1994)
[24] Watkins, S. J.; Bhattal, A. S.; Francis, N.; Turner, J. A.; Whitworth, A. P., A new prescription for viscosity in Smoothed Particle Hydrodynamics, Astron. Astrophys. Suppl. Ser., 119, 177 (1996)
[25] Brookshaw, L., A method of calculating radiative heat diffusion in particle simulations, Proc. Astron. Soc. Aust., 6, 207 (1985)
[26] J. J. Monaghan, 1995, Heat conduction with discontinuous conductivity, Applied Mathematics Reports and Preprints, 95/18, Monash University, Melbourne, Australia; J. J. Monaghan, 1995, Heat conduction with discontinuous conductivity, Applied Mathematics Reports and Preprints, 95/18, Monash University, Melbourne, Australia
[27] Schoenberg, I. J., Contributions to the problem of approximation of equidistant data by analytic functions, Q. Appl. Math., 4, 45 (1946) · Zbl 0061.28804
[28] Monaghan, J. J.; Lattanzio, J. C., A refined particle method for astrophysical problems, Astron. Astrophys., 149, 135 (1985) · Zbl 0622.76054
[29] J. P. Morris, 1996, Analysis of Smoothed Particle Hydrodynamics with Applications, Monash University, Melbourne, Australia; J. P. Morris, 1996, Analysis of Smoothed Particle Hydrodynamics with Applications, Monash University, Melbourne, Australia
[30] Epstein, N.; Masliyah, J. H., Creeping flow through clusters of spheroids and elliptical cylinders, Chem. Enj. J., 3, 169 (1972)
[31] Drummond, J. E.; Tahir, M. I., Laminar viscous flow through regular arrays of parallel solid cylinders, Int. J. Multiphase Flow, 10, 515 (1984) · Zbl 0598.76035
[32] Jackson, G. W.; James, D. F., The permeability of fibrous porous media, Can. J. Chem. Eng., 64, 364 (1986)
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.