Fast Calculation for Particle Interactions in SPH Simulations: Outlined Sub-domain Technique
A simple and easy algorithm is presented for a fast calculation of kernel functions which required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. Present proposed algorithm improves the Linked-list algorithm and adopts the Pair-Wise Interaction technique, which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The algorithm is easy to be implemented without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, smoothing length and total amount of particles are conducted to show the effectiveness of the present technique. A compact formulation is proposed for practical usage.
[1] L. B. Lucy, "Numerical approach to testing the fission hypothesis,"
Astronomical Journal, vol. 82, pp. 1013-1024, 1977.
[2] R. A. Gingold and J. J. Monaghan, "Smoothed particle hydrodynamics:
theory and application to non-spherical stars," Monthly Notices of the
Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
[3] H. H. Bui, K. Sako, and R. Fukagawa, "Numerical simulation of
soil-water interaction using smoothed particle hydrodynamics (SPH)
method," Journal of Terramechanics, vol. 44(5), pp. 339-346, 2007.
[4] S. Potapov, B. Maurel, A. Combescure, and J. Fabisk, "Modeling
accidental-type fluid-structure interaction problems with the SPH
method," Computers & Structures, vol. 87(11-12), pp. 721-734, 2009.
[5] N. Grenier, M. Antuono, A. Colagrossi, D. Le Touze, and B. Alessandrini,
"An Hamiltonian interface SPH formulation for multi-fluid and free
surface flows," Journal of Computational Physics, vol. 228(22), pp.
8380-8393, 2009.
[6] G. R. Liu and M. B. Liu, Smoothed particle hydrodynamics: a meshfree
particle method. World Scientific Publishing Co. Pte. Ltd., 2007.
[7] R. W. Hockney, S. P. Goel, and J. W. Eastwood, "A 10000 particle
molecular dynamics model with long range forces," Chemical Physics
Letters, vol. 21(3), pp. 589-591, 1973.
[8] G. Gerardi and D. Molteni, "Parallelization of a smoothed particle
hydrodynamic code for simulation of shocks in accretion disks,"
Memorie Societa Astronomica Italiana, vol. 4, pp. 46-54, 2003.
[9] A. W. Appel, "An efficient program for many-body simulations," SIAM
Journal on Scientific and Statistical Computing, vol. 6(1), pp. 85-103,
1985.
[10] L. Hernquist, "Hierarchical N-body methods," Computer Physics
Communications, vol. 48, pp. 107-115, 1988.
[11] L. Hernquist and N. Katz, "TreeSPH - A unification of SPH with the
Hierarchical Tree method," The Astrophysical Journal Supplement Series,
vol. 70, pp. 419-446, 1989.
[12] M. S. Warren and J. K. Salmon, "A portable parallel particle
program," Computer Physics Communications, vol. 87, pp. 266-290,
1995.
[13] R. W. Hockney and J. W. Eastwood, Computer simulations using
particles, Adamhilger, New York, 1988.
[14] H. Riffert, H. Herold, O. Flebbe, and H. Ruder, "Numerical aspects of the
smoothed particle hydrodynamics method for simulating accretion
disks," Computer Physics Communications, vol. 89, pp. 1-16, 1995.
[15] J. J. Monaghan, "Why particle methods work (hydrodynamics)," SIAM
Journal on Scientific and Statistical Computing, vol. 3, pp. 422-433,
1982.
[16] J. J. Monaghan and J. C. Lattanzio, "A refined particle method for
astrophysical problems," Astronomy and Astrophysics, vol. 149, pp.
135-143, 1985.
[17] J. C. Lattanzio, J. J. Monaghan, H. Pongracic, and M. P. Schwartz,
"Controlling penetration," SIAM Journal on Scientific and Statistical
Computing, vol. 7(2), pp. 591-598, 1986.
[18] J. J. Monaghan, "On the problem of penetration in particle methods,"
Journal of Computational Physics, vol. 82, pp. 1-15, 1989.
[19] J. J. Monaghan and R. A. Gingold, "Shock simulation by the particle
method of SPH," Journal of Computational Physics, vol. 52, pp. 374-389,
1983.
[20] G. A. Sod, "A survey of several finite difference methods for systems of
hyperbolic conservation laws," Journal of Computational Physics, vol. 27,
pp. 1-31, 1978.
[1] L. B. Lucy, "Numerical approach to testing the fission hypothesis,"
Astronomical Journal, vol. 82, pp. 1013-1024, 1977.
[2] R. A. Gingold and J. J. Monaghan, "Smoothed particle hydrodynamics:
theory and application to non-spherical stars," Monthly Notices of the
Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
[3] H. H. Bui, K. Sako, and R. Fukagawa, "Numerical simulation of
soil-water interaction using smoothed particle hydrodynamics (SPH)
method," Journal of Terramechanics, vol. 44(5), pp. 339-346, 2007.
[4] S. Potapov, B. Maurel, A. Combescure, and J. Fabisk, "Modeling
accidental-type fluid-structure interaction problems with the SPH
method," Computers & Structures, vol. 87(11-12), pp. 721-734, 2009.
[5] N. Grenier, M. Antuono, A. Colagrossi, D. Le Touze, and B. Alessandrini,
"An Hamiltonian interface SPH formulation for multi-fluid and free
surface flows," Journal of Computational Physics, vol. 228(22), pp.
8380-8393, 2009.
[6] G. R. Liu and M. B. Liu, Smoothed particle hydrodynamics: a meshfree
particle method. World Scientific Publishing Co. Pte. Ltd., 2007.
[7] R. W. Hockney, S. P. Goel, and J. W. Eastwood, "A 10000 particle
molecular dynamics model with long range forces," Chemical Physics
Letters, vol. 21(3), pp. 589-591, 1973.
[8] G. Gerardi and D. Molteni, "Parallelization of a smoothed particle
hydrodynamic code for simulation of shocks in accretion disks,"
Memorie Societa Astronomica Italiana, vol. 4, pp. 46-54, 2003.
[9] A. W. Appel, "An efficient program for many-body simulations," SIAM
Journal on Scientific and Statistical Computing, vol. 6(1), pp. 85-103,
1985.
[10] L. Hernquist, "Hierarchical N-body methods," Computer Physics
Communications, vol. 48, pp. 107-115, 1988.
[11] L. Hernquist and N. Katz, "TreeSPH - A unification of SPH with the
Hierarchical Tree method," The Astrophysical Journal Supplement Series,
vol. 70, pp. 419-446, 1989.
[12] M. S. Warren and J. K. Salmon, "A portable parallel particle
program," Computer Physics Communications, vol. 87, pp. 266-290,
1995.
[13] R. W. Hockney and J. W. Eastwood, Computer simulations using
particles, Adamhilger, New York, 1988.
[14] H. Riffert, H. Herold, O. Flebbe, and H. Ruder, "Numerical aspects of the
smoothed particle hydrodynamics method for simulating accretion
disks," Computer Physics Communications, vol. 89, pp. 1-16, 1995.
[15] J. J. Monaghan, "Why particle methods work (hydrodynamics)," SIAM
Journal on Scientific and Statistical Computing, vol. 3, pp. 422-433,
1982.
[16] J. J. Monaghan and J. C. Lattanzio, "A refined particle method for
astrophysical problems," Astronomy and Astrophysics, vol. 149, pp.
135-143, 1985.
[17] J. C. Lattanzio, J. J. Monaghan, H. Pongracic, and M. P. Schwartz,
"Controlling penetration," SIAM Journal on Scientific and Statistical
Computing, vol. 7(2), pp. 591-598, 1986.
[18] J. J. Monaghan, "On the problem of penetration in particle methods,"
Journal of Computational Physics, vol. 82, pp. 1-15, 1989.
[19] J. J. Monaghan and R. A. Gingold, "Shock simulation by the particle
method of SPH," Journal of Computational Physics, vol. 52, pp. 374-389,
1983.
[20] G. A. Sod, "A survey of several finite difference methods for systems of
hyperbolic conservation laws," Journal of Computational Physics, vol. 27,
pp. 1-31, 1978.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63252", author = "Buntara Sthenly Gan and Naohiro Kawada", title = "Fast Calculation for Particle Interactions in SPH Simulations: Outlined Sub-domain Technique", abstract = "A simple and easy algorithm is presented for a fast calculation of kernel functions which required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. Present proposed algorithm improves the Linked-list algorithm and adopts the Pair-Wise Interaction technique, which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The algorithm is easy to be implemented without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, smoothing length and total amount of particles are conducted to show the effectiveness of the present technique. A compact formulation is proposed for practical usage.
", keywords = "Technique, fluid simulation, smoothing particle hydrodynamic (SPH), particle interaction.", volume = "6", number = "3", pages = "352-7", }
