Numerical simulation of particle motion using a combined MacCormack and immersed boundary method
Authors: 
P. Zhang, A. BenardAuthors Info & Claims
Pages 524 - 546
Abstract
A numerical approach is presented for the direct numerical simulation of particle motion that combines the MacCormack scheme and the immersed boundary method. It exhibits the advantageous features of the explicit MacCormack scheme which is second-order accurate in time and space with simplicity in programing. The approach solves the compressible Navier-Stokes equations and uses the immersed boundary method to tackle the interactions between the fluid and the suspended particles. The force due to the interaction of two phases is computed via an elastic forcing method. The numerical approach is validated using uniform flow past a stationary circular cylinder, sedimentation of circular discs, and particle motion (orientation and translation) in unidirectional flows. Results are also compared to simulation obtained from a mixture model for solid particles for the same flow conditions.
References
[1]
M.A.H.M. Adib, K. Osman, R.P. Jong, Analysis of blood flow into the main artery via mitral valve: fluid structure interaction model, in: International Conference on Science and Social Research, 2010.
[2]
ANSYS¿ Academic Research, Release 14.0, 2012.
[3]
S.P. Autal, R.T. Lahey, J.E. Flaherty, Analysis of phase distribution in fully developed laminar bubbly two-phase flow, Int. J. Multiph. Flow, 7 (1991) 635-652.
[4]
R.P. Beyer, A computational model of the cochlea using the immersed boundary method, J. Comput. Phys., 98 (1992) 145-162.
[5]
A.J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys., 2 (1967) 12-26.
[6]
E. Fadlun, R. Verzicco, P. Orlandi, J. Mohd-Yusof, Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161 (2000) 35-60.
[7]
A. Fogelson, C. Peskin, A fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles, J. Comput. Phys., 79 (1988) 50-69.
[8]
D. Goldstein, R. Handler, L. Sirovich, Modeling a no-slip flow boundary with an external force field, J. Comput. Phys., 105 (1993) 354-366.
[9]
R. Glowinski, T.-W. Pan, T. Hesla, D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiph. Flow, 25 (1999) 755-794.
[10]
K. Höfler, S. Schwarzer, Navier-Stokes simulation with constraint forces: finite-difference method for particle-laden flows and complex geometries, Phys. Rev. E, 61 (2000) 7146-7160.
[11]
M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, 1975.
[12]
G.B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. A, 102 (1922) 161-179.
[13]
D.D. Joseph, A.F. Fortes, T.S. Lundgreen, P. Singh, Nonlinear mechanics of fluidization of beds of spheres cylinders and disks in water, in: Advances in Multiphase Flow and Related Problems, SIAM, 1987, pp. 101-122.
[14]
J. Kim, D. Kim, H. Choi, An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171 (2001) 132-150.
[15]
Y. Kim, S. Lim, S. Raman, O.P. Simonetti, A. Friedman, Blood flow in a compliant vessel by the immersed boundary method, Ann. Biomed. Eng., 37 (2009) 927-942.
[16]
Y. Kim, C.S. Peskin, 2-D parachute simulation by the immersed boundary method, SIAM J. Sci. Comput., 28 (2006) 2294-2312.
[17]
S.J. Kovacs, D.M. McQueen, C.S. Peskin, Modeling cardiac fluid dynamics and diastolic function, Philos. Trans. R. Soc. Lond. Ser. A, 359 (2001) 1299-1314.
[18]
M.-C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000) 705-719.
[19]
C. Liu, X. Zheng, C. Sung, Preconditioned multigrid methods for unsteady incompressible flows, J. Comput. Phys., 139 (1998) 35-57.
[20]
R.W. MacCormack, The effect of viscosity in hypervelocity impact cratering, 1969.
[21]
D.M. McQueen, C.S. Peskin, Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity, in: Mechanics for a New Millennium, Proceedings of the International Conference on Theoretical and Applied Mechanics, Kluwer Academic Publishers, Norwell, MA, 2001.
[22]
R. Mittal, G. Iaccarino, Immersed boundary methods, Annu. Rev. Fluid Mech., 37 (2005) 239-261.
[23]
M. Miyoshi, K. Mori, Y. Nakamura, Numerical simulation of parachute inflation process by IB method, J. Jpn. Soc. Aeronaut. Space Sci., 57 (2009) 419-425.
[24]
J. Mohd-Yosof, Combined immersed boundary/B-spline methods for simulation of flow in complex geometries, Annu. Res. Briefs Cent. Turbul. Res. (1997) 317-328.
[25]
Y. Mori, C.S. Peskin, Implicit second order immersed boundary methods with boundary mass, Comput. Methods Appl. Mech. Eng. (2008) 2049-2067.
[26]
D.H. Sharp, An overview of Rayleigh-Taylor instability, Physica D, 12 (1984) 3-18.
[27]
F. Pacull, A numerical study of the immersed boundary method and application to blood flow, University of Houston, 2006.
[28]
N. Patankar, P. Singh, D. Joseph, R. Glowinski, T.-W. Pan, A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiph. Flow, 26 (2000) 1509-1524.
[29]
C.S. Peskin, Flow patterns around heart valves: a digital computer method for solving the equations of motion, Albert Einstein College of Medicine, 1972.
[30]
C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977) 220-252.
[31]
C.S. Peskin, The immersed boundary method, Acta Numer., 11 (2002) 479-518.
[32]
A. Perrin, H.H. Hu, An explicit finite-difference scheme for simulation of moving particles, J. Comput. Phys., 212 (2006) 166-187.
[33]
S.I. Rubinow, J.B. Keller, The transverse force on a spinning sphere moving in a viscous fluid, J. Fluid Mech., 11 (1961) 447-459.
[34]
E. Saiki, S. Biringen, Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. Comput. Phys., 123 (1996) 450-465.
[35]
G. Segré, A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1, J. Fluid Mech., 14 (1962) 115-135.
[36]
G. Segré, A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2, J. Fluid Mech., 14 (1962) 136-157.
[37]
J.C. Tannehill, D.A. Anderson, R.H. Pletcher, Computational Fluid Mechanics and Heat Transfer, Taylor & Francis, Washington, DC, 1997.
[38]
M. Uhlmann, First experiments with the simulation of particulate flows, CIEMAT, Madrid, Spain, 2003.
[39]
M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys., 209 (2005) 448-476.
[40]
E.J. Vigmond, D.M. McQueen, C.S. Peskin, The cable as a basis for a mechanoelectric whole heart model, Int. J. Bioelectromagn., 5 (2003) 183-184.
[41]
M.M. Zdravkovich, Flow Around Circular Cylinder. Volume 1: Fundamental, Oxford Univ. Press, 1997.
[42]
C. Lee, Stability characteristics of the virtual boundary method in three-dimensional applications, J. Comput. Phys., 184 (2003) 559-591.
- Numerical simulation of particle motion using a combined MacCormack and immersed boundary method
Recommendations
An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application
The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier-Stokes (N-S) equations in the IB method are ...
An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry
A sharp-interface Immersed Boundary Method (IBM) is developed to simulate density-stratified turbulent flows in complex geometry using a Cartesian grid. The basic numerical scheme corresponds to a central second-order finite difference method, third-...
Immersed boundary method for the simulation of 2D viscous flow based on vorticity-velocity formulations
A new immersed boundary method based on vorticity-velocity formulations for the simulation of 2D incompressible viscous flow is proposed in present paper. The velocity and vorticity are respectively divided into two parts: one is the velocity and ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Copyright © Elsevier Inc.
Publisher
Academic Press Professional, Inc.
United States
Publication History
Published: 01 August 2015
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 24 Dec 2024