A Spectral-Element Method for Particulate Stokes Flow

Journal of Computational Physics

Volumn 156, Issue 2, 1999, Pages 360-381

  Pozrikidis, C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Boundary element methods; Boundary integral methods; Particulate flow; Spectral element methods; Stokes flow

Indexed keywords

ANGULAR VELOCITY; BOUNDARY ELEMENT METHOD; EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; ITERATIVE METHODS; LINEAR SYSTEMS; NUMERICAL METHODS; SAILING VESSELS; SUSPENSIONS (FLUIDS);

BOUNDARY INTEGRAL METHODS; BOUNDARY-ELEMENT METHODS; DISCRETIZATIONS; FORCE AND TORQUES; ITERATIVE SOLUTIONS; ORTHOGONAL COLLOCATION METHODS; PARTICULATE FLOWS; RIGID PARTICLES; SPECTRAL ELEMENT METHOD; STOKES FLOWS;

INTEGRAL EQUATIONS;

EID: 0000802336     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6375     Document Type: Article

References (41)

1. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Martinus-Nijhoff, Dordrecht, 1973).
2. S. Kim and S. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heineman, London, 1991).
3. A. Z. Zinchenko, M. A. Rother, and R. H. Davis, A novel boundary-integral algorithm for viscous interaction of deformable particles, Phys. Fluids 9, 1493 (1997).
4. C. Pozrikidis, Interfacial dynamics for Stokes flow, J. Comput. Phys., to appear.
5. H. A. Barnes, M. F. Edwards, and L. V. Woodcock, Applications of computer simulations to dense suspension rheology, Chem. Eng. Sci. 42, 591 (1987).
6. J. F. Brady and G. Bossis, Stokesian dynamics, Annu. Rev. Fluid Mech. 20, 111 (1988).
7. A. J. C. Ladd, Hydrodynamic transport coefficients of random dispersions of hard spheres, J. Chem. Phys. 95, 3484 (1990).
8. J. F. Morris and J. F. Brady, Pressure-driven flow of a suspension: Buoyancy effects, Int. J. Multiphase Flow 24, 105 (1998).
9. C. Chang and R. L. Powell, Dynamic simulations of bimodal suspensions of hydrodynamically interacting spherical particles, J. Fluid Mech. 253, 1 (1993).
10. C. Chang and R. L. Powell, Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow, J. Fluid Mech. 281, 51 (1994).
11. D. I. Dratler and W. R. Schowalter, Dynamic simulation of suspensions of non-Brownian hard spheres, J. Fluid Mech. 325, 53 (1996).
12. I. L. Claeys and J. F. Brady, Suspensions of prolate spheroids in Stokes flow. 1. Dynamics of a finite number of particles in an unbounded fluid, J. Fluid Mech. 251, 411 (1993).
13. A. S. Sangani and G. Mo, Inclusion of lubrication forces in dynamic simulations, Phys. Fluids 6, 1653 (1994).
14. G. Mo and A. S. Sangani, An O(N) algorithm for Stokes and Laplace interactions of particles, Phys. Fluids 8, 1990 (1996).
15. A. J. C. Ladd, Sedimentation of homogeneous suspensions of non-Brownian spheres, Phys. Fluids 9, 491 (1996).
16. H. H. Hu, Direct numerical simulation of flows of solid-liquid mixtures, Int. J. Multiphase Flow 22, 335 (1996).
17. G. K. Youngren and A. Acrivos, Stokes flow past a particle of arbitrary shape: A numerical method of solution, J. Fluid Mech. 69, 377 (1975).
18. T. Tran-Cong, N. Phan-Thien, and A. L. Graham, Stokes problems of multiparticle systems: Periodic arrays, Phys. Fluids A 2, 666 (1990).
19. N. Phan-Thien, T. Tran-Cong, and A. L. Graham, Shear flow of periodic arrays of particle clusters, J. Fluid Mech. 228, 275 (1991).
20. M. S. Ingber, Dynamic simulation of the hydrodynamic interaction among immersed particles in Stokes flow, Int. J. Numer. Methods in Fluids 10, 791 (1990).
21. N. Phan-Thien and S. Kim, Microstructures in Elastic Media; Principles and Computational Methods (Oxford Univ. Press, New York, 1994).
22. H. Power and G. Miranda, Second kind integral equation formulation of Stokes flow past a particle of arbitrary shape, SIAM J. Appl. Math. 47, 689 (1987).
23. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge Univ. Press, Cambridge, UK, 1992).
24. X.-J. Fan, N. Phan-Thien, and R. Zheng, Completed double-layer boundary-element method for periodic suspensions, Z. Angew. Math. Phys. 49, 167 (1998).
25. M. S. Ingber and L. A. Mondy, Direct second-kind boundary-integral formulation for Stokes flow problems, Comput. Mech. 11, 11 (1993).
26. J. M. Occhialini, G. P. Muldowney, and J. J. L. Higdon, Boundary integral/spectral element approaches to the Navier-Stokes equations, Int. J. Numer. Methods in Fluids 15, 1361 (1992).
27. G. P. Muldowney and J. J. L. Higdon, A spectral boundary element approach to three-dimensional Stokes flow, J. Fluid Mech. 298, 167 (1995).
28. C. Pozrikidis, Computation of periodic Green's functions of Stokes flow, J. Eng. Math. 30, 79 (1996).
29. G. E. Karniadakis and R. D. Henderson, Spectral element methods for incompressible flow, in The Handbook of Fluid Dynamics, edited by Johnson (CRC Press, Boca Raton, FL, 1998), Vol. 29-1, p. 41.
30. T. F. Chan, Deflated decomposition of solutions of nearly singular systems. SIAM J. Numer. Anal. 21, 738 (1984).
31. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (SIAM, Philadelphia, 1997).
32. K. E. Atkinson, The Numerical Solution of Integral Equations of the First Kind (Cambridge Univ. Press, Cambridge, UK, 1998).
33. N. Phan-Thien and D. L. Tullock, Completed double-layer boundary element method in elasticity and Stokes flow: Distributed computing through PVM, Comput. Mech. 14, 370 (1994).
34. G. H. Wannier, A contribution to the hydrodynamics of lubrication, Q. Appl. Math. 8, 1 (1950).
35. G. A. L. Van De Vorst, Integral formulation to simulate the viscous sintering of a two-dimensional lattice of periodic unit cells, J. Eng. Math. 30, 97 (1996).
36. R. Charles and C. Pozrikidis, Effect of the dispersed phase viscosity on the simple shear flow of suspensions of liquid drops, J. Fluid Mech. 365, 205 (1998).
37. A. Greenbaum and A. Mayo, Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions, J. Comput. Phys. 145, 731 (1998).
38. M. Dubiner, Spectral methods on triangles and other domains, J. Sci. Comput. 6, 345 (1991).
39. S. J. Sherwin and G. E. Karniadakis, A triangular spectral element method - Applications to the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng. 123, 189 (1995).
40. W. Heinrichs, Spectral collocation on triangular elements, J. Comput. Phys. 145, 743 (1998).
41. G. K. Batchelor, Transport properties of two-phase materials with random structure, Annu. Rev. Fluid Mech. 6, 227 (1974).