Symmetric boundary condition for the MPS method with surface tension model. (English) Zbl 1521.76680
Summary: In order to supplement the investigation of boundary conditions for the MPS method, a general computational algorithm of symmetric boundary condition for MPS is presented to simulate the symmetric problems. By the MPS method with the symmetric boundary condition (the SBC-MPS method), only half or quarter of the full computational domain needs to be set up, thus, the computational cost is able to be slashed dramatically. In the SBC-MPS method, mirror particles are introduced, which will be arranged symmetrically according to the positions of real liquid particles near to the symmetric plane, but not involved in the solution of physical properties. The function of these mirror particles is to compensate the values for the calculation of real liquid particles. As numerical tests, various of problems including two-dimensional Poiseuille Flow, three-dimensional dam-break, and some surface tension dominant problems, such as droplet wetting / impinging to a solid surface and binary droplets collision have been systematically studied by the SBC-MPS method. As a result, the algorithm shows good robustness, stability and accuracy, which demonstrates a great potential to improve the computational efficiency for dealing with symmetric problems.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
Keywords:
symmetric boundary condition; surface tension; computational efficiency; moving particle semi-implicit methodReferences:
| [1] | Woolfson, M. M., Smoothed particle hydrodynamics, Orig Evol Sol Syst (2004) |
| [2] | Koshizuka, S.; Oka, Y., Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nucl Sci Eng, 123, 421-434 (1996) |
| [3] | Gambaruto, A. M., Computational haemodynamics of small vessels using the Moving Particle Semi-implicit (MPS) method, J Comput Phys, 302, 68-96 (2015) · Zbl 1349.76937 |
| [4] | Yasumura, Y.; Yamaji, A.; Furuya, M.; Ohishi, Y.; Duan, G., Investigation on influence of crust formation on VULCANO VE-U7 corium spreading with MPS method, Ann Nucl Energy, 107, 119-127 (2017) |
| [5] | Liu, Q. X.; Sun, Z. G.; Sun, Y. J.; Chen, X.; Xi, G., Numerical investigation of liquid dispersion by hydrophobic/hydrophilic mesh packing using particle method, Chem Eng Sci, 202, 447-461 (2019) |
| [6] | Shibata, K.; Koshizuka, S.; Sakai, M.; Tanizawa, K., Transparent boundary condition for simulating nonlinear water waves by a particle method, Ocean Eng, 38, 1839-1848 (2011) |
| [7] | Sun, Z.; Xi, G.; Chen, X., A numerical study of stir mixing of liquids with particle method, Chem Eng Sci, 64, 341-350 (2009) |
| [8] | Chen, X.; Xi, G.; Sun, ZG., Improving stability of MPS method by a computational scheme based on conceptual particles, Comput Methods Appl Mech Eng, 278, 254-271 (2014) · Zbl 1423.76361 |
| [9] | Sun, Z.; Djidjeli, K.; Xing, J. T.; cheng, F., Modified MPS method for the 2D fluid structure interaction problem with free surface, Comput Fluids, 122, 47-65 (2015) · Zbl 1390.76769 |
| [10] | Khayyer, A.; Gotoh, H.; Shimizu, Y., A projection-based particle method with optimized particle shifting for multiphase flows with large density ratios and discontinuous density fields, Comput Fluids, 179, 356-371 (2019) · Zbl 1411.76138 |
| [11] | Yang, S. S.; Derakhshan, S.; Kong, F. Y., Theoretical, numerical and experimental prediction of pump as turbine performance, Renew Energy, 48, 507-513 (2012) |
| [12] | Kimura, T.; Yoshida, Y.; Hashimoto, T.; Shimagaki, M., Numerical simulation for vortex structure in a turbopump inducer: close relationship with appearance of cavitation instabilities, J Fluids Eng Trans ASME, 130, 0511041-0511049 (2008) |
| [13] | Ma, Y.; Li, Y.; Xie, F.; Wang, L.; Zhu, K., Numerical investigation on sealing behaviors of an extremely high-speed two-stage impellers structure in cryogenic rockets, Asia-Pac J Chem Eng, 13, 1-13 (2018) |
| [14] | Iga, Y.; Yoshida, Y., Numerical analysis of controlling cavitation instabilities in tandem cascades, Trans Jpn Soc Aeronaut Sp Sci, 54, 137-143 (2011) |
| [15] | Lastiwka, M.; Basa, M.; Quinlan, N. J., Permeable and non-reflecting boundary conditions in SPH, Int J Numer Methods Fluids, 61, 709-724 (2009) · Zbl 1421.76182 |
| [16] | Tezduyar, T. E.; Sathe, S.; Schwaab, M.; Conklin, B. S., Arterial fluid mechanics modeling with the stabilized space – time fluid – structure interaction technique, Int J Numer Methods Fluids, 601-629 (2008) · Zbl 1230.76054 |
| [17] | Shakibaeinia, A.; Jin, Y. C., MPS-based mesh-free particle method for modeling open-channel flows, J Hydraul Eng, 137, 1375-1384 (2011) |
| [18] | Sun, Z.; Chen, X.; Xi, G.; Liu, L.; Chen, X., Mass transfer mechanisms of rotary atomization: A numerical study using the moving particle semi-implicit method, Int J Heat Mass Transfer, 105, 90-101 (2017) |
| [19] | Shibata, K.; Koshizuka, S.; Murotani, K.; Sakai, M.; Masaie, I., Boundary conditions for simulating Karman vortices using the MPS method, J Adv Simul Sci Eng, 2, 235-254 (2015) |
| [20] | Li, D.; Sun, Z.; Chen, X.; Xi, G.; Liu, L., Analysis of wall boundary in moving particle semi-implicit method and a novel model of fluid-wall interaction, Int J Comput Fluid Dyn, 29, 199-214 (2015) · Zbl 07516248 |
| [21] | Libersky, L. D.; Petschek, A. G.; Carney, T. C.; Hipp, J. R.; Allahdadi, F. A., High strain lagrangian hydrodynamics a three-dimensional SPH code for dynamic material response, J Comput Phys, 109, 67-75 (1993) · Zbl 0791.76065 |
| [22] | Cummins, S. J.; Rudman, M., An SPH projection method, J Comput Phys, 152, 584-607 (1999) · Zbl 0954.76074 |
| [23] | Bazilevs, Y.; Hsu, M.; Kiendl, J.; Wüchner, R.; Bletzinger, K., 3D simulation of wind turbine rotors at full scale. Part II: fluid – structure interaction modeling with composite blades, Int J Numer Methods Fluids, 65, 236-253 (2011) · Zbl 1428.76087 |
| [24] | Mayrhofer, A.; Ferrand, M.; Kassiotis, C.; Violeau, D.; Morel, FX., Unified semi-analytical wall boundary conditions in SPH: analytical extension to 3-D, Numer Algorithms, 68, 15-34 (2015) · Zbl 1309.76166 |
| [25] | Kulasegaram, S.; Bonet, J.; Lewis, R. W.; Profit, M., A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications, Comput Mech, 33, 316-325 (2004) · Zbl 1067.74072 |
| [26] | Mitsume, N.; Yoshimura, S.; Murotani, K.; Yamada, T., Explicitly represented polygon wall boundary model for the explicit MPS method, Comput Part Mech, 2, 73-89 (2015) |
| [27] | Christov, C. I.; Marinova, R. S.; Marinov, TT., Identifying the stationary viscous flows around a circular cylinder at high Reynolds numbers, Lecture notes in computer science (Including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 4818 LNCS, 175-183 (2008) · Zbl 1229.76028 |
| [28] | Khayyer, A.; Gotoh, H., Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure, Coastal Eng, 56, 419-440 (2009) |
| [29] | Khayyer, A.; Gotoh, H., A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method, Appl Ocean Res, 32, 1, 124-131 (2010) |
| [30] | Khayyer, A.; Gotoh, H., Enhancement of stability and accuracy of the moving particle semi-implicit method, J Comput Phys, 230, 3093-3118 (2011) · Zbl 1316.76084 |
| [31] | Khayyer, A.; Gotoh, H., A 3D higher order Laplacian model for enhancement and stabilization of pressure calculation in 3D MPS-based simulations, Appl Ocean Res, 37, 120-126 (2012) |
| [32] | Tsuruta, N.; Khayyer, A.; Gotoh, H., Space potential particles to enhance the stability of projection-based particle methods, Int J Comput Fluid Dyn, 29, 100-119 (2015) · Zbl 07514817 |
| [33] | Wang, L.; Khayyer, A.; Gotoh, H.; Jiang, Q.; Zhang, C., Enhancement of pressure calculation in projection-based particle methods by incorporation of background mesh scheme, Appl Ocean Res, 86, 320-339 (2019) |
| [34] | Tamai, T.; Koshizuka, S., Least squares moving particle semi-implicit method, Comput Part Mech, 1, 3, 277-305 (2014) |
| [35] | Duan, G.; Yamaji, A.; Koshizuka, S.; Chen, B., The truncation and stabilization error in multiphase moving particle semi-implicit method based on corrective matrix: Which is dominant?, Comput Fluids, 190, 254-273 (2019) · Zbl 1496.76100 |
| [36] | Matsunaga, T.; Södersten, A.; Shibata, K.; Koshizuka, S., Improved treatment of wall boundary conditions for a particle method with consistent spatial discretization, Comput Methods Appl Mech Eng, 358, Article 112624 pp. (2020) · Zbl 1441.76093 |
| [37] | Gao, W.; Matsunaga, T.; Duan, G.; Koshizuka, S., A coupled 3D isogeometric/least-square MPS approach for modeling fluid-structure interactions, Comput Methods Appl Mech Eng, 373, Article 113538 pp. (2021) · Zbl 1506.74401 |
| [38] | Khayyer, A.; Gotoh, H., Enhancement of performance and stability of MPS mesh-free particle method for multiphase flows characterized by high density ratios, J Comput Phys, 242, 211-233 (2013) · Zbl 1314.76036 |
| [39] | Li, G.; Oka, Y.; Furuya, M., Experimental and numerical study of stratification and solidification/melting behaviors, Nucl Eng Des, 272, 109-117 (2014) |
| [40] | Li, X.; Oka, Y., Numerical simulation of the SURC-2 and SURC-4 MCCI experiments by MPS method, Ann Nucl Energy, 73, 46-52 (2014) |
| [41] | Kawahara, T.; Oka, Y., Ex-vessel molten core solidification behavior by moving particle semi-implicit method, J Nucl Sci Technol, 49, 1156-1164 (2012) |
| [42] | Duan, G.; Chen, B.; Zhang, X.; Wang, Y., A multiphase MPS solver for modeling multi-fluid interaction with free surface and its application in oil spill, Comput Methods Appl Mech Eng, 320, 133-161 (2017) · Zbl 1439.76004 |
| [43] | Luo, M.; Khayyer, A.; Lin, P., Particle methods in ocean and coastal engineering, Appl Ocean Res, 114, Article 102734 pp. (2021) |
| [44] | Sun, Z.; Zhang, G. Y.; Zong, Z.; Djidjeli, K.; Xing, JT., Numerical analysis of violent hydroelastic problems based on a mixed MPS-mode superposition method, Ocean Eng, 179, 285-297 (2019) |
| [45] | Masuda, M.; Sasahara, Y.; Minami, K.; Tezdogan, T.; Incecik, A., Use of the Mps method to estimate the energy conversion efficiency of the owc-wec (first report), Ocean Eng, 188, Article 106133 pp. (2019) |
| [46] | Gotoh, H.; Khayyer, A., On the state-of-the-art of particle methods for coastal and ocean engineering, Coastal Eng J, 60, 79-103 (2018) |
| [47] | Khayyer, A.; Gotoh, H.; Shimizu, Y.; Nishijima, Y., A 3D Lagrangian meshfree projection-based solver for hydroelastic fluid-structure interactions, J Fluids Struct, 105, Article 103342 pp. (2011) |
| [48] | Zhang, G.; Zhao, W.; Wan, D., Partitioned MPS-FEM method for free-surface flows interacting with deformable structures, Appl Ocean Res, 114, Article 102775 pp. (2021) |
| [49] | Xie, F.; Zhao, W.; Wan, D., Numerical simulations of liquid-solid flows with free surface by coupling IMPS and DEM, Appl Ocean Res, 114, Article 102771 pp. (2021) |
| [50] | Khayyer, A.; Gotoh, H.; Falahaty, H.; Shimizu, Y., An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions, Comput Phys Commun, 232, 139-164 (2018) · Zbl 07694794 |
| [51] | Khayyer, A.; Tsuruta, N.; Shimizu, Y.; Gotoh, H., Multi-resolution MPS for incompressible fluid-elastic structure interactions in ocean engineering, Appl Ocean Res, 82, 397-414 (2019) |
| [52] | Khayyer, A.; Shimizu, Y.; Gotoh, H.; Nagashima, K., A coupled incompressible SPH-Hamiltonian SPH solver for hydroelastic FSI corresponding to composite structures, Appl Math Model, 94, 242-271 (2021) · Zbl 1481.74155 |
| [53] | Hori, C.; Gotoh, H.; Ikari, H.; Khayyer, A., GPU-acceleration for Moving Particle Semi-Implicit method, Comput Fluids, 51, 174-183 (2011) · Zbl 1271.76264 |
| [54] | Chen, X.; Sun, Z. G.; Liu, L.; Xi, G., Improved MPS method with variable-size particles, Int J Numer Methods Fluids, 80, 6, 358-374 (2016) |
| [55] | Khayyer, A.; Tsuruta, N.; Shimizu, Y.; Gotoh, H., Multi-resolution MPS for incompressible fluid-elastic structure interactions in ocean engineering, Appl Ocean Res, 82, 397-414 (2019) |
| [56] | Tanaka, M.; Cardoso, R.; Bahai, H., Multi-resolution MPS method, J Comput Phys, 359, 106-136 (2018) · Zbl 1383.76388 |
| [57] | Li, M. K.; Zhang, A. M.; Ming, F. R.; Sun, P. N.; Peng, YX., An axisymmetric multiphase SPH model for the simulation of rising bubble, Comput Methods Appl Mech Eng, 366, Article 113039 pp. (2020) · Zbl 1442.76085 |
| [58] | Liang, Y.; Sun, Z.; Xi, G.; Liu, L., Numerical models for heat conduction and natural convection with symmetry boundary condition based on particle method, Int J Heat Mass Transf, 88, 433-444 (2015) |
| [59] | Gotoh, H.; Khayyer, A.; Ikari, H.; Arikawa, T.; Shimosako, K., On enhancement of Incompressible SPH method for simulation of violent sloshing flows, Appl Ocean Res, 46, 104-115 (2014) |
| [60] | Kondo, M.; Suzuki, K.; Koshizuka, S.; Takimoto, M., Surface tension model using inter-particle force in particle method, (Proceedings of the 5th joint ASME/JSME fluids engineering summer conference, FEDSM 2007, 1 SYMPOSIA (2007)), 93-98 |
| [61] | Liu, K. S.; Sheu, T. W.H.; Hwang, Y. H.; Ng, KC., High-order particle method for solving incompressible Navier-Stokes equations within a mixed Lagrangian-Eulerian framework, Comput Methods Appl Mech Eng, 325, 77-101 (2017) · Zbl 1439.76019 |
| [62] | Antuono, M.; Marrone, S.; Colagrossi, A.; Bouscasse, B., Energy balance in the δ-SPH scheme, Comput Methods Appl Mech Eng, 289, 209-226 (2015) · Zbl 1423.76360 |
| [63] | Khayyer, A.; Gotoh, H.; Shimizu, Y.; Gotoh, K., On enhancement of energy conservation properties of projection-based particle methods, Eur J Mech B/Fluids, 66, 20-37 (2017) · Zbl 1408.76414 |
| [64] | You, Y.; Khayyer, A.; Zheng, X.; Gotoh, H.; Ma, Q., Enhancement of δ-SPH for ocean engineering applications through incorporation of a background mesh scheme, Appl Ocean Res, 110, Article 102508 pp. (2021) |
| [65] | Martin, J. C.; Moyce, W. J., Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane, Philosophical Transactions of the Royal Society A, 244, 312-324 (1952) |
| [66] | Chatzikyriakou, D.; Walker, S. P.; Hale, C. P.; Hewitt, GF., The measurement of heat transfer from hot surfaces to non-wetting droplets, Int J Heat Mass Transf, 54, 1432-1440 (2011) · Zbl 1211.80007 |
| [67] | Wildeman, S.; Visser, C. W.; Sun, C.; Lohse, D., On the spreading of impacting drops, J Fluid Mech, 805, 636-655 (2016) |
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