Simulation of Multi-Phase Medium Using BPM-SPH Hybrid Method

Document Type : Original Research

Authors
M. Yazdani 1
A. Fakhimi 2
M. Mazhary 3
1 Assistant Professor, Department of civil and environmental engineering, Tarbiat Modares university of Tehran
2 Associate Professor, Department of Civil and Environmental Engineering, Tarbiat Modares University of Tehran
3 Ph.D. Candidate, Department of Civil and Environmental Engineering, Tarbiat Modares University of Tehran
Abstract
The precision and speed of numerical simulations of physical phenomena has led to their increasing use in designing and research applications. These precision and speed are owed to the improvements in numerical methods and significant advancements in computing power of CPUs and GPUs.

Particle-based methods are some of the most recently developed numerical simulation methods. Development of these methods has been long delayed due to the need for a relatively high computational effort.

Particle-based methods can be considered as a subset of Meshless Methods. In nonlinear computational methods, mathematical equations in the problem domain are estimated only by nodes, and contrary to the case about the nodes in FEM and FDM methods, there is no need for these nodes to be connected to each other by a mesh. If the nodes are particles that carry physical properties, such as mass and stiffness, and simulations proceed on the basis of updating trajectory and physical properties of particles, then the method is called a particle-based method. Particle-based methods include molecular dynamics (MD), Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH), and Lattice Boltzmann Method (LBM). The number of studies and computer codes developed based on these methods has grown dramatically over the past two decades.

Among particle-based methods, DEM method is mainly used to model solid objects and fractures and in some cases it has been used to model granular materials like soil. While most of the applications of SPH method include numerical solution of the Navier-Stokes equations in fluid dynamic problems. Despite their differences, both DEM and SPH methods are particle-based methods and so there have been successful attempts to integrate them into a single application.

In current study, a computer code called “QUANTA” is introduced. In this software, the researchers have tried to integrate the SPH method with another particle-based method called Bonded Particle Method (BPM). BPM is based on DEM and was originally developed to model rock and soil mechanics phenomena. The main modification applied to DEM is the ability to consider cohesion among particles, which plays a significant role in simulating the behavior of rocks and soils.

QUANTA is being developed with the goal of providing a tool to simulate two-dimensional solid, fluid, and multi-phased interactive environments for research purposes. In this software, the solid environment is modeled using the BPM algorithm and the fluid environment is modeled using the SPH algorithm by solving Navier-Stokes equations. Depending on the problem at hand, BPM and SPH particles interact with each other by equations based on momentum or pressure. The code is developed using Visual C ++ programming language and has the ability to perform parallel computations with a remarkable speed.

To verify the software, a few simple and frequently used problems in the literature were chosen. A cantilever beam was modeled and loaded to verify BPM part of the software. Poiseuille and shear cavity problems were used to verify the SPH part. In order to verify the interaction of these two algorithms, a solid cylinder was modeled once in a wind tunnel travelling at supersonic speeds and then against the flow of a viscous fluid. According to the results of these numerical modellings, the software can be deemed successful in simulating the sample problems.

While simulation with particle methods requires more computational effort than common methods such as finite element and finite difference, the particle-based and micromechanical nature of these methods and their ability to model large-scale deformations and complex behaviors has, in many cases, made them logical choices for simulation. As the next steps of this study, the authors are developing new equations for interaction and equations of state to improve the software performance.

Keywords

Subjects

[1] L. XiangZhe, F. JingCun, Y. Hao, Z. YinBo and W. HengAn, "Lattice Boltzmann method simulations about shale gas flow in contracting nano-channels," International Journal of Heat and Mass Transfer, vol. 122, pp. 1210-1221, 2018.
[2] A. Colagrossi and M. Landrini, "Numerical simulation of interfacial flows by smoothed particle," Journal of computational physics, vol. 191, pp. 448-475, 2003.
[3] P. Langston, U. Tüzün and D. Heyes, "Discrete element simulation of granular flow in 2D and 3D hoppers: dependence of discharge rate and wall stress on particle interactions," Chemical Engineering Science, vol. 50, pp. 967-987, 1995.
[4] Q. Lin, A. Fakhimi, M. Haggerty and J. F. Labuz, "Initiation of tensile and mixed-mode fracture in sandstone," International Journal of Rock Mechanics & Mining Sciences, vol. 46, pp. 489-497, 2009.
[5] C. Antoci, M. Gallati and S. Sibilla, "Numerical simulation of fluid-structure interaction by SPH," Computers & Structures, vol. 85, pp. 879-890, 2007.
[6] M. Lanari and A. Fakhimi, "Numerical study of contributions of shock wave and gas penetration toward induced rock damage during blasting," Computational Particle Mechanics, vol. 2, no. 2, pp. 197-208, 2015.
[7] D. O. Potyondy and P. A. Cundall, "A bonded-particle model for rock," International Journal of Rock Mechanics and Mining Sciences, vol. 41, no. 8, p. 1329–1364, 2004.
[8] L. B. Lucy, "Numerical approach to testing the fission hypothesis," Astronomical Journal, vol. 82, pp. 1013-1024, 1977.
[9] R. A. Gingold and J. J. Monaghan, "Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical stars," Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
[10] G. Liu and M. Liu, Smoothed particle hydrodynamics a meshfree particle method, World Scientific Publishing Company, 2003.
[11] J. J. Monaghan, "Smoothed particle hydrodynamics," Annual Review of Astronomical and Astrophysics, vol. 30, pp. 543-574, 1992.
[12] R. A. Gingold and J. J. Monaghan, "Kernel estimates as a basis for general particle method in hydrodynamics," Journal of Computational Physics, vol. 46, pp. 429-453, 1982.
[13] P. J. Morris, "A study of the stability properties of SPH," Publications of the Astronomical Society of Australia, vol. 13, no. 1, pp. 97-102, 1994.
[14] J. J. Monaghan, "Why particle methods work (hydrodynamics)," SIAM Journal on Scientific and Statistical Computing, vol. 3, pp. 422-433, 1982.
[15] L. D. Libersky and A. G. Petscheck, "Smoothed particle hydrodynamics with strength of materials," in H. Trease, J. Fritts and W. Crowley (ed.): Proceedings of The Next Free Lagrange Conference, NY, 1991.
[16] J. J. Monaghan, "Particle methods for hydrodynamics," Computer Physics Report, vol. 3, pp. 71-124, 1985.
[17] J. J. Monaghan, "Simulating Free Surface Flow with SPH," Journal of Computational Physics, vol. 110, no. 2, pp. 399-406, 1994.
[18] J. J. Monaghan, "An introduction to SPH," Computer Physics Communications, vol. 48, pp. 89-96, 1988.
[19] D. Fulk, A numerical analysis of smoothed particle hydrodynamics, PhD. Thesis, Air Force Institute of Technology, 1994.
[20] J. J. Monaghan and R. A. Gingold, "Shock simulation by the particle method of SPH," Journal of Computational Physics, vol. 52, pp. 374-381, 1983.
[21] S. Adami, X. Y. Hu and N. A. Adams, "A generalized wall boundary condition for smoothed particle hydrodynamics," Journal of Computational Physics, vol. 231, pp. 7057-7075, 2012.
[22] G. McKinley, "MITOPENCOURSEWARE," 2013. [Online]. Available: https://ocw.mit.edu/courses/mechanical-engineering/2-25-advanced-fluid-mechanics-fall-2013/equations-of-viscous-flow/MIT2_25F13_Couet_and_Pois.pdf. [Accessed 2019].
[23] H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Longman Scientific & Technical., 1995, p. pp. 192–206.
[24] I. Federico, S. Marrone, A. Colagrossi, F. Aristodemo and M. Antuono, "mulating 2D open-channel flows through an SPH model," European Journal of Mechanics B/Fluids, vol. 34, pp. 35-46, 2012.
Modares Civil Engineering journal
Volume 19, Issue 4
November and December 2019
Pages 187-200