High order computation of the history term in the equation of motion for a spherical particle in a fluid

Journal of Scientific Computing

Volumn 21, Issue 2, 2004, Pages 129-143

  Alexander, P ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Equation of motion; High order method; History term

Indexed keywords

COMPUTATIONAL METHODS; EQUATIONS OF MOTION; INTEGRAL EQUATIONS; RUNGE KUTTA METHODS; UNSTEADY FLOW; VISCOUS FLOW;

HIGH ORDER METHOD; HISTORY TERM; SPHERICAL PARTICLES; UNSTEADY MOTIONS;

FLUID DYNAMICS;

EID: 3042757999     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOMP.0000030072.32108.d9     Document Type: Review

References (29)

1. AEA Technology Engineering Software Limited (1999). CFX-TASCflow Theory Documentation, AEA, Waterloo.
2. Alexander, P., and de la Torre, A. (2003). A program for the simulation and analysis of open atmospheric balloon soundings. Comput. Phys. Comm. 151, 96-120.
3. Auton, T. R., Hunt, J. C. R., and Prud'homme, M. (1988). The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241-257.
4. Babiano, A., Cartwright, J. H. E., Piro, O., and Provenzale, A. (2000). Dynamics of a small neutrally buoyant sphere in a fluid and targeting in hamiltonian systems. Phys. Rev. Lett. 84, 5764-5767.
5. Basset, A. B. (1888). On the motion of a sphere in a viscous liquid. Philos. Trans. Roy. Soc. London 179, 43-63.
6. Boussinesq, J. (1885). Sur la resistance qu'oppose un liquide indefini en repos. C. R. Acad. Sci. Paris 100, 935-937.
7. Butcher, J. C. (1994). Runge-Kutta methods in modern computation, part I: Fundamental concepts. Comput. Phys. 8, 411-415.
8. Butcher, J. C. (1994). Runge-Kutta methods in modern computation, part II: Implicit methods and related applications. Comput. Phys. 8, 512-517.
9. Chang, E. J., and Maxey, M. R. (1994). Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion. J. Fluid Mech. 277, 347-379.
10. Chang, E. J., and Maxey, M. R. (1995). Unsteady flow about a sphere at low to moderate Reynolds number. Part 2. Accelerated motion. J. Fluid Mech. 303, 133-153.
11. Coimbra, C. F. M., and Rangel, R. H. (1998). General solution of the particle momentum equation in unsteady Stokes flow. J. Fluid Mech. 370, 53-72.
12. Ferziger, J. H., and Perić, M. (2002). Computational Methods for Fluid Dynamics, Springer, Berlin.
13. Li, L., and Michaelides, E. E. (1992). The magnitude of Basset forces in unsteady multi-phase flow computations. J. Fluids Eng. 114, 417-419.
14. Lovalenti, P. M., and Brady, J. F. (1993). The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561-605.
15. Lovalenti, P. M., and Brady, J. F. (1993). The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number. J. Fluid Mech. 256, 607-614.
16. Maxey, M. R. (1993). The equation of motion for a small rigid sphere in a nonuniform or unsteady flow. Gas-solid flows (ASME) 166, 57-62.
17. Maxey, M. R. (2000). Note on initial conditions when using the history term. Personal communication.
18. Maxey, M. R., and Riley, J. J. (1983). Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883-889.
19. Mei, R. (1994). Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J. Fluid Mech. 270, 133-174.
20. Mei, R., and Adrian, R. J. (1992). Flow past a spehre with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 323-341.
21. Mei, R., Lawrence, C. J., and Adrian, R. J. (1991). Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. J. Fluid Mech. 233, 613-631.
22. Michaelides, E. E. (1992). A novel way of computing the Basset term in unsteady multi-phase flow computations. Phys. Fluids A 4, 1579-1582.
23. Michaelides, E. E. (1997). Review-The transient equation of motion for particles, bubbles, and droplets. J. Fluids Eng. 119, 233-247.
24. Oseen, C. W. (1927). Hydrodynamik, Akademische Verlagsgesellschaft, Leipzig.
25. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in Fortran: The Art of Scientific Computing, Cambridge University Press, Cambridge.
26. Reeks, M. W., and McKee, S. (1984). The dispersive effects of Basset history forces on particle motion in a turbulent flow. Phys. Fluids 27, 1573-1582.
27. Tatom, F. B. (1988). The Basset term as a semiderivative. Appl. Sci. Res. 45, 283-285.
28. Taylor, G. I. (1928). The forces on a body placed in a curved or converging stream of fluid. Proc. Roy. Soc. London Ser. A 120, 260-283.
29. Vojr, D. J., and Michaelides, E. E. (1994). Effect of the history term on the motion of rigid spheres in a viscous fluid. Intl. J. Multiphase Flow 20, 547-556.