Unstructured moving particle pressure mesh (UMPPM) method for incompressible isothermal and non-isothermal flow computation. (English) Zbl 1423.76324
Summary: In this work, we intend to address the limitation of our earlier particle method, namely the Moving Particle Pressure Mesh (MPPM) method in handling arbitrary-shaped flow boundaries. The application of the Cartesian pressure mesh system adopted in our original MPPM method, which serves as the main key in recovering the divergence-free velocity condition for incompressible flow in the framework of particle method, is rather limited to rectangular flow domain. Here, the hybrid unstructured pressure mesh is adopted to remove the geometrical constraint of our earlier MPPM method. Coupled with the moving particle strategy in the Moving Particle Semi-implicit (MPS) method, the new method is named as the Unstructured Moving Particle Pressure Mesh (UMPPM) method in the current work. A consistent Laplacian model, namely the Consistent Particle Method (CPM) recently reported in the open literature is incorporated as well in the framework of UMPPM for discretizing the viscous term on the scattered particle cloud, while its implicit form is solved in the current work for overall robustness. Finally, we shall verify our UMPPM method with a series of benchmark solutions (for isothermal and non-isothermal flows) available from the literatures, including those obtained from the commercial code. It is appealing to find that the numerical solutions of UMPPM compare well with the benchmark solutions. In some cases, the accuracy of our UMPPM is better than that of the existing particle method such as Smoothed Particle Hydrodynamics (SPH).
MSC:
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 76M28 | Particle methods and lattice-gas methods |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 76Dxx | Incompressible viscous fluids |
Keywords:
moving particle semi-implicit (MPS); consistent particle method (CPM); moving particle pressure mesh (MPPM); particle-in-cell (PIC); unstructured mesh; incompressible flowSoftware:
PICINReferences:
| [1] | Koshizuka, S.; Oka, Y., Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nucl. Sci. Eng., 123, 421-434 (1996) |
| [2] | Nakanishi, Y.; Fujii, T.; Kawaguchi, S., Numerical and experimental investigations of the flow in a stationary Pelton bucket, J. Fluid Sci. Technol., 4, 3, 490-499 (2009) |
| [3] | Sun, Z. G.; Liang, Y. Y.; Xi, G., Numerical simulation of the flow in straight blade agitator with the MPS method, Internat. J. Numer. Methods Fluids, 67, 1960-1972 (2011) · Zbl 1426.76571 |
| [4] | Chen, R.; Tian, W.; Su, G. H.; Qiu, S.; Ishiwatari, Y.; Oka, Y., Numerical investigation on bubble dynamics during flow boiling using moving particle semi-implicit method, Nucl. Eng. Des., 240, 3830-3840 (2010) |
| [5] | Yashiro, S.; Okabe, T.; Matsushima, K., A numerical approach for injection molding of short-fiber-reinforced plastics using a particle method, Adv. Compos. Mater., 20, 503-517 (2011) |
| [6] | Kawahara, T.; Oka, Y., Ex-vessel molten core solidification behavior by moving particle semi-implicit method, J. Nucl. Sci. Technol., 49, 12, 1156-1164 (2012) |
| [7] | Kon, T.; Natsu, S.; Ueda, S.; Inoue, R.; Ariyama, T., Influence of physical properties of melt on liquid dripping in packed bed analyzed by MPS Method, ISIJ Int., 53, 4, 590-597 (2013) |
| [8] | Ng, K. C.; Ng, E. Y.K.; Lam, W. H., Lagrangian simulation of steady and unsteady laminar mixing by plate impeller in a cylindrical vessel, Ind. Eng. Chem. Res., 52, 29, 10004-10014 (2013) |
| [9] | Ng, K. C.; Ng, E. Y.K., Laminar mixing performances of baffling, shaft eccentricity and unsteady mixing in a cylindrical vessel, Chem. Eng. Sci., 104, 960-974 (2013) |
| [10] | Shibata, K.; Koshizuka, S., Numerical analysis of shipping water impact on a deck using a particle method, Ocean Eng., 34, 585-593 (2007) |
| [11] | Kakuda, K.; Ushiyama, Y.; Obara, S.; Toyotani, J.; Matsuda, S.; Tanaka, H.; Katagiri, K., Flow simulations in a liquid ring pump using a particle method, Comput. Model. Eng. Sci., 66, 3, 215-226 (2010) |
| [12] | Hirata, N.; Anzai, K., Numerical simulation of shrinkage formation of pure Sn casting using particle method, Mater. Trans., 52, 10, 1931-1938 (2011) |
| [13] | Kon, T.; Natsui, S.; Ueda, S.; Inoue, R.; Ariyama, T., Numerical simulation of dripping behavior of droplet in packed bed using particle method, ISIJ Int., 52, 9, 1565-1573 (2012) |
| [14] | Okabe, T.; Matsutani, H.; Honda, T.; Yashiro, S., Numerical simulation of microscopic flow in a fiber bundle using the moving particle semi-implicit method, Composites A, 43, 1765-1774 (2012) |
| [15] | Koshizuka, S.; Nobe, A.; Oka, Y., Numerical analysis of breaking waves using the moving particle semi-implicit method, Internat. J. Numer. Methods Fluids, 26, 751-769 (1998) · Zbl 0928.76086 |
| [18] | Shakibaeinia, A.; Jin, Y. C., Lagrangian multiphase modeling of sand discharge into still water, Adv. Water Resour., 48, 55-67 (2012) |
| [19] | Sun, Z. G.; Xi, G.; Chen, X., A numerical study of stir mixing of liquids with particle method, Chem. Eng. Sci., 64, 341-350 (2009) |
| [20] | Sakai, M.; Shigeto, Y.; Sun, X.; Aoki, T.; Saito, T.; Xiong, J.; Koshizuka, S., Lagrangian-Lagrangian modeling for a solid-liquid flow in a cylindrical tank, Chem. Eng. J., 200-202, 663-672 (2012) |
| [21] | Li, D.; Sun, Z. G.; 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. (2015) · Zbl 07516248 |
| [22] | Xie, H.; Koshizuka, S.; Oka, Y., Modelling of a single drop impact onto liquid film using particle method, Internat. J. Numer. Methods Fluids, 45, 1009-1023 (2004) · Zbl 1079.76614 |
| [23] | Zhang, S.; Morita, K.; Fukuda, K.; Shirakawa, N., An improved MPS method for numerical simulations of convective heat transfer problems, Internat. J. Numer. Methods Fluids, 51, 31-47 (2006) · Zbl 1146.80008 |
| [24] | Lee, B. H.; Park, J. C.; Kim, M. H.; Hwang, S. C., Step-by-step improvement of MPS method in simulating violent free-surface motions and impact loads, Comput. Methods Appl. Mech. Engrg., 200, 1113-1125 (2011) · Zbl 1225.76234 |
| [25] | Akimoto, H., Numerical simulation of the flow around a planing body by MPS method, Ocean Eng., 64, 72-79 (2013) |
| [26] | Hwang, Y. H., A moving particle method with embedded pressure mesh (MPPM) for incompressible flow calculations, Numer. Heat Transfer B, 60, 370-398 (2011) |
| [27] | Ng, K. C.; Hwang, Y. H.; Sheu, T. W.H., On the accuracy assessment of Laplacian models in MPS, Comput. Phys. Comm., 185, 10, 2412-2426 (2014) · Zbl 1360.35049 |
| [28] | Ng, K. C.; Hwang, Y. H.; Sheu, T. W.H.; Yu, C. H., Moving particle level-set (MPLS) method for incompressible multiphase flow computation, Comput. Phys. Comm., 196, 317-334 (2015) |
| [29] | Harlow, F. H., A machine calculation method for hydrodynamic problems, (Technical Report LAMS-1956 (1955), Los Alamos Scientific Laboratory: Los Alamos Scientific Laboratory Los Alamos, New Mexico) |
| [30] | Kelly, D. M.; Chen, Q.; Zang, J., PICIN: A particle-in-cell solver for incompressible free surface flows with two-way fluid-solid coupling, SIAM J. Sci. Comput., 37, 3, B404-B424 (2015) · Zbl 1323.35129 |
| [31] | Matsunaga, T.; Shibata, K.; Murotani, K.; Koshizuka, S., Hybrid grid-particle method for fluid mixing simulation, Comput. Part. Mech., 2, 233-246 (2015) |
| [32] | Liu, J.; Koshizuka, S.; Oka, Y., A hybrid particle-mesh method for viscous, incompressible, multiphase flows, J. Comput. Phys., 202, 65-93 (2005) · Zbl 1061.76069 |
| [33] | Ye, T.; Mittal, R.; Udaykumar, H. S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., 156, 209-240 (1999) · Zbl 0957.76043 |
| [34] | Ng, K. C., A collocated finite volume embedding method for simulation of flow past stationary and moving body, Comput. & Fluids, 38, 2, 347-357 (2009) · Zbl 1237.76090 |
| [35] | Koh, C. G.; Gao, M.; Luo, C., A new particle method for simulation of incompressible free surface flow problems, Internat. J. Numer. Methods Engrg., 89, 1582-1604 (2012) · Zbl 1242.76272 |
| [36] | Tanaka, M.; Masunaga, T., Stabilization and smoothing of pressure in MPS method by quasi-compressibility, J. Comput. Phys., 229, 4279-4290 (2010) · Zbl 1334.76121 |
| [37] | Kondo, M.; Koshizuka, S., Improvement of stability in moving particle semi-implicit method, Internat. J. Numer. Methods Fluids, 65, 638-654 (2011) · Zbl 1428.76155 |
| [38] | Natsui, S.; Takai, H.; Kumagai, T.; Kikuchi, T.; Suzuki, R. O., Stable mesh-free moving particle semi-implicit method for direct analysis of gas-liquid two-phase flow, Chem. Eng. Sci., 111, 286-298 (2014) |
| [40] | Jin, M.; Chen, Q., Accelerating fast fluid dynamics with a coarse-grid projection scheme, HVAC R Res., 20, 8, 932-943 (2014) |
| [41] | Jin, M.; Zuo, W.; Chen, Q., Improvements of fast fluid dynamics for simulating airflow in buildings, Numer. Heat Transfer B, 62, 6, 419-438 (2012) |
| [43] | Souto-Iglesias, A.; Macia, F.; Gonzalez, L. M.; Cercos-Pita, J. L., On the consistency of MPS, Comput. Phys. Comm., 184, 3, 732-745 (2013) · Zbl 1307.76031 |
| [44] | Koh, C. G.; Luo, M.; Gao, M.; Bai, W., Modelling of liquid sloshing with constrained floating baffle, Comput. Struct., 122, 270-279 (2013) |
| [45] | Gao, M., Numerical simulation of liquid sloshing in rectangular tanks using consistent particle method and experimental verification (2011), National University of Singapore: National University of Singapore Singapore, (Ph.D. thesis) |
| [46] | Jasak, H., Error analysis and estimation for the finite volume method with applications to fluid flows (1996), Imperial College London (University of London): Imperial College London (University of London) UK, (Ph.D. thesis) |
| [48] | Ng, K. C.; Yusoff, M. Z.; Ng, E. Y.K., Multigrid solution of Euler equations using high-resolution NVD differencing scheme for unstructured meshes, Prog. Comput. Fluid Dyn., 6, 7, 389-401 (2006) · Zbl 1189.76370 |
| [49] | Ng, K. C.; Yusoff, M. Z.; Ng, E. Y.K., Parametric study of an improved GAMMA differencing scheme based on normalized-variable formulation for low-speed flow with artificial compressibility technique, Numer. Heat Transfer B, 50, 6, 561-584 (2006) |
| [50] | Ng, K. C.; Yusoff, M. Z.; Ng, E. Y.K., Higher-order bounded differencing schemes for compressible and incompressible flows, Internat. J. Numer. Methods Fluids, 53, 1, 57-80 (2007) · Zbl 1149.76658 |
| [51] | Ng, K. C.; Ng, E. Y.K.; Yusoff, M. Z.; Lim, T. K., Applications of high-resolution schemes based on normalized variable formulation for 3D indoor airflow simulations, Internat. J. Numer. Methods Engrg., 73, 7, 948-981 (2008) · Zbl 1171.76036 |
| [52] | Yoon, H. Y.; Koshizuka, S.; Oka, Y., A particle-gridless hybrid method for incompressible flows, Internat. J. Numer. Methods Fluids, 30, 407-424 (1999) · Zbl 0948.76067 |
| [53] | Shakibaeinia, A.; Jin, Y. C., MPS mesh-free particle method for multiphase flows, Comput. Methods Appl. Mech. Engrg., 229-232, 13-26 (2012) · Zbl 1253.76106 |
| [54] | Tabbara, M.; Blacker, T.; Belytschko, T., Finite element derivative recovery by moving least square interpolants, Comput. Methods Appl. Mech. Engrg., 117, 211-223 (1994) · Zbl 0848.73072 |
| [55] | Colagrossi, A.; Landrini, M., Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. Comput. Phys., 191, 2, 448-475 (2003) · Zbl 1028.76039 |
| [56] | Van der Vorst, H. A., Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13, 2, 631-644 (1992) · Zbl 0761.65023 |
| [57] | Khayyer, A.; Gotoh, H., Development of CMPS method for accurate water-surface tracking in breaking waves, Coastal Eng. J., 50, 2, 179-207 (2008) |
| [58] | Ellero, M.; Serrano, M.; Espanol, P., Incompressible smoothed particle hydrodynamics, J. Comput. Phys., 226, 1731-1752 (2007) · Zbl 1121.76050 |
| [59] | Adami, S.; Hu, X. Y.; Adams, N. A., A transport-velocity formulation for smoothed particle hydrodynamics, J. Comput. Phys., 241, 292-307 (2013) · Zbl 1349.76659 |
| [60] | Ghia, U.; Ghia, K. N.; Shin, C. T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 387-411 (1982) · Zbl 0511.76031 |
| [61] | Erturk, E.; Dursun, B., Numerical solutions of 2D steady incompressible flow in a driven skewed cavity, ZAMM J. Appl. Math. Mech., 87, 377-392 (2007) · Zbl 1115.76055 |
| [62] | Armaly, B. F.; Durst, F.; Pereira, J. C.F.; Schonung, B., Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 127, 473-496 (1983) |
| [63] | Shu, C.; Xue, H.; Zhu, Y. D., Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method, Int. J. Heat Mass Transfer, 44, 3321-3333 (2001) · Zbl 1006.76548 |
| [64] | Peng, Y.; Chew, Y. T.; Shu, C., Numerical simulation of natural convection in a concentric annulus between a square outer cylinder and a circular inner cylinder using the Taylor-series-expansion and least-squares-based lattice Boltzmann method, Phys. Rev. E, 67, Article 026701 pp. (2003) |
| [65] | Moukalled, F.; Acharya, S., Natural convection in the annulus between concentric horizontal circular and square cylinders, J. Thermophys Heat Transfer, 10, 3, 524-531 (1996) |
| [66] | 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 Transfer, 88, 433-444 (2015) |
| [67] | Kuehn, T. H.; Goldstein, R. J., An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders, J. Fluid Mech., 74, 4, 695-719 (1976) · Zbl 0323.76071 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
