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==Applications==
Through the past years, the MPS method has been applied in a wide range of engineering applications including Nuclear Engineering (e.g. [https://dx.doi.org/10.1016/S0029-5493(98)00270-2 Koshizuka et al., 1999]; Koshizuka and Oka, 2001; [https://dx.doi.org/10.1016/j.nucengdes.2005.01.011 Xie et al., 2005]), Coastal Engineering (e.g. [https://dx.doi.org/10.1142/S0578563405001239 Gotoh et al., 2005]; [https://dx.doi.org/10.1016/j.coastaleng.2005.10.007 Gotoh and Sakai, 2006]), Environmental Hydraulics (e.g. [https://dx.doi.org/10.1002/fld.2132 Shakibaeina and Jin, 2009]; [http://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0001275 Nabian and Farhadi, 2016]; [https://doi.org/10.1061/(ASCE)IR.1943-4774.0001211 Xu and Jin, 2017]), Ocean Engineering ([https://dx.doi.org/10.1016/j.oceaneng.2005.12.012 Shibata and Koshizuka, 2007]; [https://doi.org/10.1007%2Fs00773-007-0260-y Sueyoshi et al., 2008]; [https://doi.org/10.1016/j.oceaneng.2019.04.054 Xu and Jin, 2019]; [https://doi.org/10.1016/j.oceaneng.2022.111569 Zuo et al. 2022]), Structural Engineering (e.g. [https://doi.org/10.1007%2Fs004660000216 Chikazawa et al., 2001]), Mechanical Engineering (e.g. [https://dx.doi.org/10.1016/S0017-9310(02)00011-X Heo et al., 2002]; [https://archive.today/20130223115811/http://link.aip.org/link/?PHFLE6/21/032106/1 Sun et al., 2009]), Bioengineering (e.g. [http://www.jamstec.go.jp/esc/publication/journal/jes_vol.5/pdf/JES5_21-Tsubota.pdf Tsubota et al., 2006]) and Chemical Engineering (e.g. [https://dx.doi.org/10.1016/j.ces.2008.10.034 Sun et al., 2009]; [https://doi.org/10.1016/j.ces.2018.07.016 Xu and Jin, 2018
==Improvements==
Improved versions of MPS method have been proposed for enhancement of numerical stability (e.g. [https://archive.today/20130105131748/http://www3.interscience.wiley.com/journal/2910/abstract Koshizuka et al., 1998]; [https://dx.doi.org/10.1002/fld.1106 Zhang et al., 2005]; [https://dx.doi.org/10.1016/j.fluiddyn.2005.12.002 Ataie-Ashtiani and Farhadi, 2006];[https://dx.doi.org/10.1002/fld.2132 Shakibaeina and Jin, 2009]; [https://doi.org/10.1016/j.cma.2019.112771 Jandaghian and Shakibaeinia, 2020]), momentum conservation (e.g. Hamiltonian MPS by [https://dx.doi.org/10.1016/j.cma.2006.12.006 Suzuki et al., 2007]; Corrected MPS by [https://dx.doi.org/10.1142/S0578563408001788 Khayyer and Gotoh, 2008]; Enhanced MPS by [https://doi.org/10.1016/j.cma.2019.112771 Jandaghian and Shakibaeinia, 2020]), mechanical energy conservation (e.g. Hamiltonian MPS by [https://dx.doi.org/10.1016/j.cma.2006.12.006 Suzuki et al., 2007]), pressure calculation (e.g. [https://dx.doi.org/10.1016/j.coastaleng.2008.10.004 Khayyer and Gotoh, 2009], [https://dx.doi.org/10.1002/fld.2207 Kondo and Koshizuka, 2010], [https://dx.doi.org/10.1016/j.apor.2010.01.001 Khayyer and Gotoh, 2010], [https://
== References ==
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* T. Xu, Y. C. Jin, Y. C. Tai, Mesh-free peridynamic coupled simulation of impacting collapse of a granular column with various heights. Physics of Fluids, 33(10), 103321, 2021.
* T. Xu, Y. C. Jin, Two-dimensional continuum modelling granular column collapse by non-local peridynamics in a mesh-free method with rheology. Journal of Fluid Mechanics, 917, A51, 2021.
* T. Xu, Y. C. Jin, Numerical study of the flow over broad-crested weirs by a mesh-free method. Journal of Irrigation and Drainage Engineering, 143(9), 04017034, 2017.
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