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1

Monaghan, J. J. "Smoothed Particle Hydrodynamics." Annual Review of Astronomy and Astrophysics 30, no. 1 (September 1992): 543–74. http://dx.doi.org/10.1146/annurev.aa.30.090192.002551.

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2

Monaghan, J. J. "Smoothed particle hydrodynamics." Reports on Progress in Physics 68, no. 8 (July 5, 2005): 1703–59. http://dx.doi.org/10.1088/0034-4885/68/8/r01.

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3

Li, Hongbin, Lixuan Zhang, Zhongxiang Shen, and Wenqing Wang. "Cone structure‒ice interaction simulation based on the common-node discrete element method–smoothed particle hydrodynamics coupling method." Advances in Engineering Technology Research 11, no. 1 (August 1, 2024): 846. http://dx.doi.org/10.56028/aetr.11.1.846.2024.

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This paper presents a novel approach utilizing the discrete element method (DEM) and smoothed particle hydrodynamics (SPH). A new fluid–structure coupling method called the common-node discrete element method–smoothed particle hydrodynamics (DS–SPH) is proposed. The DS-SPH method involves establishing a DEM and SPH method on the same node to create common-node discrete element-smoothed particle hydrodynamics (DEM-SPH, DS) particles. This enables the DEM particles to experience forces exerted by the SPH particles within their supporting region through the SPH particles located at the same node. As a result, fluid-structure interactions (FSIs) can be achieved. The interaction between the cone structure and the sea ice is investigated via this method, and the crack generation mechanism of the sea ice during the collision process is investigated.
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4

Ritchie, B. W., and P. A. Thomas. "Multiphase smoothed-particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 323, no. 3 (May 21, 2001): 743–56. http://dx.doi.org/10.1046/j.1365-8711.2001.04268.x.

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5

Cullen, Lee, and Walter Dehnen. "Inviscid smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 408, no. 2 (July 30, 2010): 669–83. http://dx.doi.org/10.1111/j.1365-2966.2010.17158.x.

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6

Tsuji, P., M. Puso, C. W. Spangler, J. M. Owen, D. Goto, and T. Orzechowski. "Embedded smoothed particle hydrodynamics." Computer Methods in Applied Mechanics and Engineering 366 (July 2020): 113003. http://dx.doi.org/10.1016/j.cma.2020.113003.

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7

Ellero, Marco, Mar Serrano, and Pep Español. "Incompressible smoothed particle hydrodynamics." Journal of Computational Physics 226, no. 2 (October 2007): 1731–52. http://dx.doi.org/10.1016/j.jcp.2007.06.019.

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8

Petschek, A. G., and L. D. Libersky. "Cylindrical Smoothed Particle Hydrodynamics." Journal of Computational Physics 109, no. 1 (November 1993): 76–83. http://dx.doi.org/10.1006/jcph.1993.1200.

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9

Tavakkol, Sasan, Amir Reza Zarrati, and Mahdiyar Khanpour. "Curvilinear smoothed particle hydrodynamics." International Journal for Numerical Methods in Fluids 83, no. 2 (June 7, 2016): 115–31. http://dx.doi.org/10.1002/fld.4261.

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10

Wang, Jingsi, Shaolin Xu, Keita Shimada, Masayoshi Mizutani, and Tsunemoto Kuriyagawa. "Smoothed particle hydrodynamics simulation and experimental study of ultrasonic machining." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 232, no. 11 (February 20, 2017): 1875–84. http://dx.doi.org/10.1177/0954405417692005.

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Hard and brittle materials like glass and ceramics are highly demanded in modern manufacturing industries. However, their superior physical and mechanical properties lead to high cost of machining. Ultrasonic machining has been regarded as one of the most suitable fabrication techniques for these kinds of materials. A smoothed particle hydrodynamics model was proposed to study the material removal mechanism of the ultrasonic machining in this study. Influences of abrasive materials and the particle shapes on the crack formation of work substrates were investigated using this smoothed particle hydrodynamics model. Experiments were also conducted to verify the simulation model. Both of the simulation and experimental results show that using hard and spherical abrasive particles is helpful to improve the material removal efficiency. This work was the first to demonstrate the crack formation mechanisms during ultrasonic machining with different abrasive particles using smoothed particle hydrodynamics, which is significant for improving the machining performance of the ultrasonic machining process.
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11

Trimulyono, Andi. "Validasi Gerakan Benda Terapung Menggunakan Metode Smoothed Particle Hydrodynamics." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 15, no. 2 (June 6, 2018): 38–43. http://dx.doi.org/10.14710/kpl.v15i2.17802.

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12

Hedayati, Ehsan, and Mohammad Vahedi. "Evaluating Impact Resistance of Aluminum 6061-T651 Plate using Smoothed Particle Hydrodynamics Method." Defence Science Journal 68, no. 3 (April 16, 2018): 251. http://dx.doi.org/10.14429/dsj.68.11635.

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Performing various experimental, theoretical, and numerical investigations for better understanding of behavioural characteristics of metals under impact loading is of primary importance. In this paper, application of smoothed particle hydrodynamics (SPH) method in impact mechanics is discussed and effective parameters on impact strength of an aluminum plate are investigated. To evaluate the accuracy of smoothed particle hydrodynamics method for simulating impact, Recht and Ipson model is first provided thoroughly for both Rosenberg analytical model and smoothed particle hydrodynamics method, and then plots of initial velocity-residual velocity and initial velocity-absorbed energy for target of aluminum 6061-T651 are presented. The derived information and simulation results expresses that the maximum error percentage of smoothed particle hydrodynamics method in compared with Rosenberg analytical model is within an acceptable range. Therefore, the results of smoothed particle hydrodynamics method verify the Rosenberg analytical model with high accuracy. Results reveal that higher initial impact velocity decreases the time of projectile penetration, and so penetration depth and length as well as the local damage rate of plate increases.
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13

Murante, G., S. Borgani, R. Brunino, and S. H. Cha. "Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 417, no. 1 (September 13, 2011): 136–53. http://dx.doi.org/10.1111/j.1365-2966.2011.19021.x.

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14

Yamamoto, Satoko, Takayuki R. Saitoh, and Junichiro Makino. "Smoothed particle hydrodynamics with smoothed pseudo-density." Publications of the Astronomical Society of Japan 67, no. 3 (April 3, 2015): 37. http://dx.doi.org/10.1093/pasj/psv006.

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15

Su, Chong, Li Da Zhu, and Wan Shan Wang. "Simulation Research on Cutting Process of Single Abrasive Grain." Advanced Materials Research 239-242 (May 2011): 3123–26. http://dx.doi.org/10.4028/www.scientific.net/amr.239-242.3123.

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Cutting processes of single abrasive grain were simulated respectively by fluid-solid interaction method and Smoothed Particle Hydrodynamics method. Advantages and disadvantages of the two methods were compared. Smoothed Particle Hydrodynamics method is superior to fluid-solid interaction method in simulating the deformation behavior of workpiece material for the motion of SPH particles. According to the simulation results, it is concluded that workpiece material occurs plastic deformation, flows to the side and front owing to the extrusion of abrasive grain, and finally forms chip in front of abrasive grain.
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16

Muhammad Haseeb, Hasan Aftab Saeed, and Imran Sajid S. Ghumman. "Numerical Simulation of Orthogonal Machining of Gallium Nitride via Smoothed Particle Hydrodynamics." NUML International Journal of Engineering and Computing 1, no. 1 (April 27, 2022): 27–38. http://dx.doi.org/10.52015/nijec.v1i1.11.

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Gallium Nitride is one of the best candidates for upcoming industrial revolution due to itssuperior electrical properties over silicon. In the present work, we investigate the chipformation, cutting force and effective stress in diamond machining of gallium nitride bysmoothed particle hydrodynamics approach based on Mohr-Coulomb material model. Thecomparison of the effective stress as reported by molecular dynamics studies and thatpredicted by the smoothed particle hydrodynamics simulation demonstrates the effectivenessof the smoothed particle hydrodynamics model.
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17

Liptai, David, and Daniel J. Price. "General relativistic smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 485, no. 1 (January 17, 2019): 819–42. http://dx.doi.org/10.1093/mnras/stz111.

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18

Springel, Volker. "Smoothed Particle Hydrodynamics in Astrophysics." Annual Review of Astronomy and Astrophysics 48, no. 1 (August 2010): 391–430. http://dx.doi.org/10.1146/annurev-astro-081309-130914.

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19

Monaghan, Joseph J., Herbert E. Huppert, and M. Grae Worster. "Solidification using smoothed particle hydrodynamics." Journal of Computational Physics 206, no. 2 (July 2005): 684–705. http://dx.doi.org/10.1016/j.jcp.2004.11.039.

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20

Ayal, S., T. Piran, R. Oechslin, M. B. Davies, and S. Rosswog. "Post‐Newtonian Smoothed Particle Hydrodynamics." Astrophysical Journal 550, no. 2 (April 2001): 846–59. http://dx.doi.org/10.1086/319769.

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21

Wong, S., and Y. Shie. "Galerkin based smoothed particle hydrodynamics." Computers & Structures 87, no. 17-18 (September 2009): 1111–18. http://dx.doi.org/10.1016/j.compstruc.2009.04.010.

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22

Price, Daniel J. "Smoothed particle hydrodynamics and magnetohydrodynamics." Journal of Computational Physics 231, no. 3 (February 2012): 759–94. http://dx.doi.org/10.1016/j.jcp.2010.12.011.

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23

Swegle, J. W., D. L. Hicks, and S. W. Attaway. "Smoothed Particle Hydrodynamics Stability Analysis." Journal of Computational Physics 116, no. 1 (January 1995): 123–34. http://dx.doi.org/10.1006/jcph.1995.1010.

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24

Trimulyono, Andi, and Ardhana Wicaksono. "Simulasi numerik large-deformation surface wave dengan smoothed particle hydrodynamics." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 15, no. 3 (February 14, 2019): 102–6. http://dx.doi.org/10.14710/kapal.v15i3.21535.

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25

Wang, Sheng, Yong Ou Zhang, and Jing Ping Wu. "Lagrangian meshfree finite difference particle method with variable smoothing length for solving wave equations." Advances in Mechanical Engineering 10, no. 7 (July 2018): 168781401878924. http://dx.doi.org/10.1177/1687814018789248.

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In a Lagrangian meshfree particle-based method, the smoothing length determines the size of the support domain for each particle. Since the particle distribution is irregular and uneven in most cases, a fixed smoothing length sometime brings too much or insufficient neighbor particles for the weight function which reduces the numerical accuracy. In this work, a Lagrangian meshfree finite difference particle method with variable smoothing length is proposed for solving different wave equations. This pure Lagrangian method combines the generalized finite difference scheme for spatial resolution and the time integration scheme for time resolution. The new method is tested via the simple wave equation and the Burgers’ equation in Lagrangian form. These wave equations are widely used in analyzing acoustic and hydrodynamic waves. In addition, comparison with a modified smoothed particle hydrodynamics method named the corrective smoothed particle method is also presented. Numerical experiments show that two kinds of Lagrangian wave equations can be solved well. The variable smoothing length updates the support domain size appropriately and allows the finite difference particle method results to be more accurate than the constant smoothing length. To obtain the same level of accuracy, the corrective smoothed particle method needs more particles in the computation which requires more computational time than the finite difference particle method.
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26

Liu, M. B., and G. R. Liu. "Restoring particle consistency in smoothed particle hydrodynamics." Applied Numerical Mathematics 56, no. 1 (January 2006): 19–36. http://dx.doi.org/10.1016/j.apnum.2005.02.012.

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27

Lastiwka, Martin, Nathan Quinlan, and Mihai Basa. "Adaptive particle distribution for smoothed particle hydrodynamics." International Journal for Numerical Methods in Fluids 47, no. 10-11 (2005): 1403–9. http://dx.doi.org/10.1002/fld.891.

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28

Dong, Xiangwei, Zengliang Li, Qi Zhang, Wei Zeng, and G. R. Liu. "Analysis of surface-erosion mechanism due to impacts of freely rotating angular particles using smoothed particle hydrodynamics erosion model." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 231, no. 12 (March 29, 2017): 1537–51. http://dx.doi.org/10.1177/1350650117700750.

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The free rotation of an angular particle during its impact on ductile surfaces is an important factor that influences the erosion mechanism. However, the phenomenon cannot be easily revealed experimentally because the incident conditions cannot be accurately controlled. In this study, a novel erosion model based on smoothed particle hydrodynamics method is proposed to simulate single and multiple impacts of particles with specified angularities on a ductile surface. The model can simulate a particle having free rotation during the impact process and initial rotation prior to the impact. The results show that the impact angle and initial orientation significantly affect the tumbling behavior, which determines the erosion mechanism. Moreover, the initial rotation is investigated by assigning an initial angular velocity to the particle at the onset of impact. The proposed smoothed particle hydrodynamics erosion model is proven to be a promising complementary method that supports experimental techniques. This study provides insight for understanding the fundamental mechanisms of surface erosion due to angular particles.
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29

LIU, M. B., G. R. LIU, and Z. ZONG. "AN OVERVIEW ON SMOOTHED PARTICLE HYDRODYNAMICS." International Journal of Computational Methods 05, no. 01 (March 2008): 135–88. http://dx.doi.org/10.1142/s021987620800142x.

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This paper presents an overview on smoothed particle hydrodynamics (SPH), which is a meshfree, particle method of Lagrangian nature. In theory, the interpolation and approximations of the SPH method and the corresponding numerical errors are analyzed. The inherent particle inconsistency has been discussed in detail. It has been demonstrated that the particle inconsistency originates from the discrete particle approximation process and is the fundamental cause for poor approximation accuracy. Some particle consistency restoring approaches have been reviewed. In application, SPH modeling of general fluid dynamics and hyperdynamics with material strength have been reviewed with emphases on (1) microfluidics and microdrop dynamics, (2) coast hydrodynamics and offshore engineering, (3) environmental and geophysical flows, (4) high-explosive detonation and explosions, (5) underwater explosions, and (6) hydrodynamics with material strength including hypervelocity impact and penetration.
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30

Daropoulos, Viktor, Matthias Augustin, and Joachim Weickert. "Sparse Inpainting with Smoothed Particle Hydrodynamics." SIAM Journal on Imaging Sciences 14, no. 4 (January 2021): 1669–705. http://dx.doi.org/10.1137/20m1382179.

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31

Wissing, Robert, Sijing Shen, James Wadsley, and Thomas Quinn. "Magnetorotational instability with smoothed particle hydrodynamics." Astronomy & Astrophysics 659 (March 2022): A91. http://dx.doi.org/10.1051/0004-6361/202141206.

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The magnetorotational instability (MRI) is an important process in driving turbulence in sufficiently ionized accretion disks. It has been extensively studied using simulations with Eulerian grid codes, but remains fairly unexplored for meshless codes. Here, we present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method with the geometric density average force expression. We performed 37 shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained turbulence can be simulated successfully with smoothed-particle hydrodynamics (SPH), with results consistent with prior work with grid-based codes, including saturation properties such as magnetic and kinetic energies and their respective stresses. In particular, for the stratified boxes, our simulations reproduce the characteristic “butterfly” diagram of the MRI dynamo with saturated turbulence for at least 100 orbits. On the contrary, traditional SPH simulations suffer from runaway growth and develop unphysically large azimuthal fields, similar to the results from a recent study with meshless methods. We investigated the dependency of MRI turbulence on the numerical Prandtl number (Pm) in SPH, focusing on the unstratified, zero net-flux case. We found that turbulence can only be sustained with a Prandtl number larger than ∼2.5, similar to the critical values for the physical Prandtl number found in grid-code simulations. However, unlike grid-based codes, the numerical Prandtl number in SPH increases with resolution, and for a fixed Prandtl number, the resulting magnetic energy and stresses are independent of resolution. Mean-field analyses were performed on all simulations, and the resulting transport coefficients indicate no α-effect in the unstratified cases, but an active αω dynamo and a diamagnetic pumping effect in the stratified medium, which are generally in agreement with previous studies. There is no clear indication of a shear-current dynamo in our simulation, which is likely to be responsible for a weaker mean-field growth in the tall, unstratified, zero net-flux simulation.
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32

Quinlan, Nathan J., and Mingming Tong. "Industrial Applications of Smoothed Particle Hydrodynamics." International Journal of Computational Fluid Dynamics 35, no. 1-2 (February 7, 2021): 1–2. http://dx.doi.org/10.1080/10618562.2021.1946946.

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33

Wang, Mengdi, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, and Bo Zhu. "Thin-film smoothed particle hydrodynamics fluid." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–16. http://dx.doi.org/10.1145/3476576.3476675.

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34

Wang, Mengdi, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, and Bo Zhu. "Thin-film smoothed particle hydrodynamics fluid." ACM Transactions on Graphics 40, no. 4 (August 2021): 1–16. http://dx.doi.org/10.1145/3450626.3459864.

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35

Kodama, T., C. E. Aguiar, T. Osada, and Y. Hama. "Entropy-based relativistic smoothed particle hydrodynamics." Journal of Physics G: Nuclear and Particle Physics 27, no. 3 (February 20, 2001): 557–60. http://dx.doi.org/10.1088/0954-3899/27/3/336.

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36

Krištof, P., B. Beneš, J. Křivánek, and O. Št'ava. "Hydraulic Erosion Using Smoothed Particle Hydrodynamics." Computer Graphics Forum 28, no. 2 (April 2009): 219–28. http://dx.doi.org/10.1111/j.1467-8659.2009.01361.x.

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37

Oxley, S., and M. M. Woolfson. "Smoothed particle hydrodynamics with radiation transfer." Monthly Notices of the Royal Astronomical Society 343, no. 3 (August 11, 2003): 900–912. http://dx.doi.org/10.1046/j.1365-8711.2003.06751.x.

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38

Kessel-Deynet, O., and A. Burkert. "Ionizing radiation in smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 315, no. 4 (July 11, 2000): 713–21. http://dx.doi.org/10.1046/j.1365-8711.2000.03451.x.

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39

Oger, L., and S. B. Savage. "Smoothed particle hydrodynamics for cohesive grains." Computer Methods in Applied Mechanics and Engineering 180, no. 1-2 (November 1999): 169–83. http://dx.doi.org/10.1016/s0045-7825(99)00054-7.

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40

Imaeda, Yusuke, and Shu‐ichiro Inutsuka. "Shear Flows in Smoothed Particle Hydrodynamics." Astrophysical Journal 569, no. 1 (April 2002): 501–18. http://dx.doi.org/10.1086/339320.

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41

Abadi, Mario G., Diego G. Lambas, and Patricia B. Tissera. "Cosmological Simulations with Smoothed Particle Hydrodynamics." Symposium - International Astronomical Union 168 (1996): 577–78. http://dx.doi.org/10.1017/s0074180900110757.

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We have developed and tested a code that computes the evolution of a mixed system of gas and dark matter in expanding world models. The gravitational forces are calculated with the Adaptative P3M algorithms developed by H. Couchmann, 1993. The calculation of gas forces follow the standard SPH formalism (Monaghan, 1989).
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42

Fulk, David A., and Dennis W. Quinn. "Hybrid Formulations of smoothed particle hydrodynamics." International Journal of Impact Engineering 17, no. 1-3 (January 1995): 329–40. http://dx.doi.org/10.1016/0734-743x(95)99859-p.

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43

Zhou, Dai, Si Chen, Lei Li, Huafeng Li, and Yaojun Zhao. "Accuracy Improvement of Smoothed Particle Hydrodynamics." Engineering Applications of Computational Fluid Mechanics 2, no. 2 (January 2008): 244–51. http://dx.doi.org/10.1080/19942060.2008.11015225.

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44

Owen, J. Michael, Jens V. Villumsen, Paul R. Shapiro, and Hugo Martel. "Adaptive Smoothed Particle Hydrodynamics: Methodology. II." Astrophysical Journal Supplement Series 116, no. 2 (June 1998): 155–209. http://dx.doi.org/10.1086/313100.

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45

OBARA, Haruki, Mariko HONDA, and Akinori KOYAMA. "Fundamental Study of Smoothed Particle Hydrodynamics." Journal of Computational Science and Technology 2, no. 1 (2008): 101–10. http://dx.doi.org/10.1299/jcst.2.101.

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46

OBARA, Haruki, Jhun SUEMURA, and Mariko HONDA. "Fundamental Study of Smoothed Particle Hydrodynamics." Journal of Computational Science and Technology 2, no. 1 (2008): 92–100. http://dx.doi.org/10.1299/jcst.2.92.

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47

Zhu, Qirong, Lars Hernquist, and Yuexing Li. "NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS." Astrophysical Journal 800, no. 1 (February 2, 2015): 6. http://dx.doi.org/10.1088/0004-637x/800/1/6.

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48

Rosswog, Stephan. "Conservative, special-relativistic smoothed particle hydrodynamics." Journal of Computational Physics 229, no. 22 (November 2010): 8591–612. http://dx.doi.org/10.1016/j.jcp.2010.08.002.

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49

Liu, M. B., G. R. Liu, and Shaofan Li. "?Smoothed particle hydrodynamics ? a meshfree method?" Computational Mechanics 33, no. 6 (May 1, 2004): 491. http://dx.doi.org/10.1007/s00466-004-0573-1.

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50

Cleary, Paul W., and Joseph J. Monaghan. "Conduction Modelling Using Smoothed Particle Hydrodynamics." Journal of Computational Physics 148, no. 1 (January 1999): 227–64. http://dx.doi.org/10.1006/jcph.1998.6118.

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