A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow

Computer Methods in Applied Mechanics and Engineering

Volumn 184, Issue 2-4, 2000, Pages 241-267

  Glowinski, Roland ^a   Pan, Tsorng Whay ^a   Hesla, Todd I ^b   Joseph, Daniel D ^b   Periaux, Jacques ^c  

^a University of Houston   (United States)

^b University of Minnesota   (United States)

^c DASSAULT AVIATION   (France)

Author keywords

Fictitious domain methods; Liquid solid mixtures; Navier Stokes equations; Particulate flow; Rayleigh Taylor instabilities

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; FLOW OF FLUIDS; HYDRODYNAMICS; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; MIXTURES; NAVIER STOKES EQUATIONS; VISCOUS FLOW;

FICTITIOUS DOMAIN METHODS; LINEARLY CONSTRAINED QUADRATIC MINIMIZATION PROBLEMS; PARTICULATE FLOW; RAYLEIGH-TAYLOR INSTABILITIES;

LAGRANGE MULTIPLIERS;

FLOW AROUND OBJECT; LAGRANGIAN ANALYSIS; LIQUID-SOLID TWO-PHASE FLOW; NAVIER-STOKES EQUATIONS; PARTICLE FLOW;

FLOW AROUND OBJECT; LAGRANGIAN ANALYSIS; NAVIER-STOKES EQUATIONS; PARTICLE MOTION; TWO PHASE FLOW;

EID: 0034646896     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00230-3     Document Type: Article

References (34)

1. Glowinski R., Pan T.-W., Périaux J. A fictitious domain method for Dirichlet problem and applications. Comput. Meth. Appl. Mech. Eng. 111:1994;283-303.
2. Glowinski R., Pan T.-W., Périaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 112:1994;133-148.
3. Glowinski R., Pan T.-W., Périaux J. A Lagrange multiplier/fictitious domain method for the Dirichlet problem. Generalization to some flow problems. Japan J. Industrial Appl. Math. 12:1995;87-108.
4. R. Glowinski, T.-W. Pan, J. Périaux, Fictitious domain methods for incompressible viscous flow around moving rigid bodies, in: J.R. Whiteman (Ed.), The Mathematics of Finite Elements and Applications, Highlight 1996, Wiley, Chichester, England, 1997 pp. 155-174.
5. R. Glowinski, T.-W. Pan, J. Périaux, A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies (I): the case where the rigid body motions are known a priori, C. R. Acad. Sci. Paris, 324 (1997) 361-369.
6. Glowinski R., Pan T.W., Périaux J. Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies. Comput. Meth. Appl. Mech. Eng. 151:1998;181-194.
7. A. Johnson, T. Tezduyar, 3-D Simulation of fluid-rigid body interactions with the number of rigid bodies reaching 100, University of Minnesota, AHPCRC preprint, 1996, pp. 96-037.
8. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25:1977;220-252.
9. Peskin C.S., McQueen D.M. Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys. 37:1980;113-132.
10. Peskin C.S. Lectures on mathematical aspects of physiology. Lectures in Appl. Math. 19:1981;69-107.
11. LeVeque R.J., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31:1994;1019-1044.
12. LeVeque R.J., Li Z. Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18:1997;709-735.
13. R. Glowinski, T.W. Pan, T. Hesla, D.D. Joseph, J. Périaux, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Internat. J. Multiphase Flow 25 (1999) 755-794.
14. B.A. Maury, A many-body lubrication model, C. R. Acad. Sci., Paris t. 325, Série I, 1997, pp. 1053-1058.
15. T.I. Hesla, The dynamical simulation of 2-D fluid/rigid body systems, unpublished notes, 1991.
16. Hu H.H. Direct simulation of flows of solid-liquid mixtures. Internat. J. Multiphase Flow. 22:1996;335-352.
17. Bertrand F., Tanguy P.A., Thibault F. A 3-D fictitious domain method for incompressible fluid flow problem. Internat. J. Numer. Meth. Fluids. 25:1997;719-736.
18. Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. 1991;Springer, New York.
19. J.E. Roberts, J.M. Thomas, Mixed and Hybrid Methods, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. II, North-Holland, Amsterdam, 1991, pp. 523-639.
20. Chorin A.J. A numerical method for solving incompressible viscous flow problem. J. Comput. Phys. 2:1967;12-26.
21. Chorin A.J. On the convergence and approximation of discrete approximation to the Navier-Stokes equations. Math. Comput. 23:1968;341-353.
22. Chorin A.J. Numerical study of slightly viscous flow. J. Fluid Mech. 57:1973;785-796.
23. Glowinski R., Pironneau O. Finite element methods for Navier-Stokes equations. Ann. Rev. Fluid Mech. 24:1992;167-204.
24. Turek S. A comparative study of time-stepping techniques for the incompressible Navier-Stokes equations: from fully implicit nonlinear schemes to semi-implicit projection methods. Internat. J. Numer. Math. Fluids. 22:1996;987-1011.
25. G.I. Marchuk, Splitting and alternate direction methods, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. I, North-Holland, Amsterdam, 1990, pp. 197-462.
26. E. Dean, R. Glowinski, A wave equation approach to the numerical solution of the Navier-Stokes equation for incompressible viscous flow, C.R. Acad. Sci. Paris, t. 325, Série I, 1997, pp. 783-791.
27. E. Dean, R. Glowinski, T.-W. Pan, A wave equation approach to the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations, in: J. De Santo (Ed.), Mathematical and numerical aspects of wave propagation, SIAM, Philadelphia, 1998, pp. 65-74.
28. Glowinski R. Numerical Methods for Nonlinear Variational Problems. 1984;Springer, New York.
29. Fortin M., Glowinski R. Augmented Lagrangian Methods. 1983;North-Holland, Amsterdam.
30. Glowinski R., LeTallec P. Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. 1989;SIAM, Philadelphia, PA.
31. Kikuchi N., Oden T.J. Contact Problems in Elasticity. 1988;SIAM, Philadelphia, PA.
32. E.J. Dean, R. Glowinski, Y.M. Kuo, M.G. Nasser, On the discretization of some second order in time differential equations, Applications to nonlinear wave problems, in: A.V. Balakrishnan (Ed.), Computational Techniques in Identification and Control of Flexible Flight Structures, Optimization Software, Inc., Los Angeles, 1990, pp. 199-246.
33. Hu H., Joseph D.D., Fortes A.F. Experiments and direct simulation of fluid particle motions. Internat. Vid. J. Eng. Res. 2:1992;17.
34. Fortes A.F., Joseph D.D., Lundgren T.S. Nonlinear mechanics of fluidization of beds of spherical particles. J. Fluid Mech. 177:1987;467-483.