Extension of Smoothed Particle Hydrodynamics (SPH), Mathematical Background of Vortex Blob Method (VBM) and Moving Particle Semi-Implicit (MPS)

Hiroshi Isshiki^{*}

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References

[1] Isshiki, H. (2011) Discrete Differential Operators on Irregular Nodes (DDIN). International Journal for Numerical Methods in Engineering, 88, 1323-1343. http://dx.doi.org/10.1002/nme.3225

[2] Gingold, R.A. and Monaghan, J.J. (1977) Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars. Monthly Notices of the Royal Astronomical Society, 181, 375-389.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1977MNRAS.181..375G&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

http://dx.doi.org/10.1093/mnras/181.3.375

[3] Lucy, L.B. (1977) A Numerical Approach to the Testing of the Fission Hypothesis. The Astronomical Journal, 82, 1013-1024.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1977AJ.....82.1013L&defaultprint=YES&filetype=.pdf

http://dx.doi.org/10.1086/112164

[4] Chorin, A.J. (1973) Numerical Study of Slightly Viscous Flow. Journal of Fluid Mechanics, 57, 785-796.

http://dx.doi.org/10.1017/S0022112073002016

[5] Yokoyama, M., Kubota, Y., Kikuchi, K., Yagawa, G. and Mochizuki, O. (2014) Some Remarks on Surface Conditions of Solid Body Plunging into Water with Particle Method. Advanced Modeling and Simulation in Engineering Sciences, 1, 2-14. http://www.amses-journal.com/content/pdf/2213-7467-1-9.pdf

[6] Ng, K.C., Hwang, Y.H. and Sheu, T.W.H. (2014) On the Accuracy Assessment of Laplacian Models in MPS. Computer Physics Communications, 185, 2412-2426.

[7] Isshiki, H., Nagata, S. and Imai, Y. (2014) Solution of Viscous Flow around a Circular Cylinder by a New Integral Representation Method (NIRM). The Association for Japan Exchange and Teaching, 2, 60-82.

file:///C:/Users/l/Downloads/983-5001-1-PB%20(2).pdf

[8] Koshizuka, S. and Oka, Y. (1996) Moving Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid. Nuclear Science and Engineering, 123, 421-434.

[9] Moscardini, L. and Dolag, K. (2011) Chapter 4: Cosmology with Numerical Simulations. In: Matarrese, S., Colpi, M., Gorini, V. and Moschella, U., Eds., Dark Matter and Dark Energy, Springer, Berlin, 217-237.

[10] Monaghan, J.J. (1992) Smoothed Particle Hydrodynamics. Annual Review of Astronomy and Astrophysics, 30, 543-573.

http://dx.doi.org/10.1146/annurev.aa.30.090192.002551

[11] Wikipedia, Burgers’ Equation. http://en.wikipedia.org/wiki/Burgers'_equation