Development and application of a parallel multigrid solver for the simulation of spreading droplets

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 8, 2008, Pages 979-989

  Gaskell, P H ^a   Jimack, P K ^a   Koh, Y Y ^a   Thompson, H M ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Multigrid; Parallel algorithms; Thin film approximation

Indexed keywords

ALGEBRA; DROPS; FINITE DIFFERENCE METHOD; FLOW OF FLUIDS; MESH GENERATION; NONLINEAR EQUATIONS; PARALLEL ALGORITHMS;

APPROXIMATION STORAGE MULTIGRID ALGORITHM; NONLINEAR LUBRICATION EQUATION;

COMPUTATIONAL FLUID DYNAMICS;

ALGEBRA; COMPUTATIONAL FLUID DYNAMICS; DROPS; FINITE DIFFERENCE METHOD; FLOW OF FLUIDS; MESH GENERATION; NONLINEAR EQUATIONS; PARALLEL ALGORITHMS;

EID: 40749153496     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1737     Document Type: Conference Paper

References (18)

1. De Gennes PG. Wetting: statics and dynamics. Reviews of Modern Physics 1985; 57:827.
2. Peurring LM, Graves DB. Spin coating over topography. IEEE Transactions on Semiconductor Manufacturing 1993; 6:72-76.
3. Gaskell PH, Jimack PK, Sellier M, Thompson HM. Efficient and accurate time-adaptive multigrid simulations of droplet spreading. International Journal for Numerical Methods in Fluids 2004; 45:1161-1186.
4. Oron A, Davis SH, Bankoff SG. Long-scale evolution of thin liquid films. Reviews of Modern Physics 1997; 69:931-980.
5. Schwartz LW. Hysteretic effects in droplet motion on heterogeneous substrates: direct numerical simulation. Langmuir 1998; 14:3440-3453.
6. Sellier M. The numerical simulation of thin film flow over heterogeneous substrates. Ph.D. Thesis, University of Leeds, U.K., 2006.
7. Schwartz LW, Eley RR. Simulation of droplet motion on low-energy and heterogeneous surfaces. Journal of Colloid and Interface Science 1998; 202:173-188.
8. Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977; 31: 333-390.
9. Brandt A. Guide to multigrid development. In Multigrid Methods, Hackbusch W, Trottenberg U (eds). Lecture Notes in Mathematics, vol, 960. Springer: Berlin, 1982; 220-312.
10. Trottenberg U, Oosterlee CW, Schüller A. Multigrid. Academic Press: New York, 2000.
11. Wesseling P. Introduction to Multigrid Methods. Wiley: New York, 1992.
12. Starov VM, Kalinin VV, Chen JD. Spreading of liquid drops over dry surfaces. Advances in Colloid and Interface Science 1994; 50:187-221.
13. Bertozzi A. The mathematics of moving contact lines in this liquid films. Notices of the AMS 1998; 45:689-697.
14. Zhornitskaya L, Bertozzi A. Positivity-preserving numerical schemes for lubrication-type equations. SIAM Journal on Numerical Analysis 2000; 37:523-555.
15. Goodyer CE, Berzins M. Parallelisation and scalability issues of a multilevel elastohydrodynamic lubrication solver. Concurrency and Computation: Practice & Experience 2007; 19:369-396.
16. Koh Y-Y. Efficient numerical solutions of droplet spreading flows. Ph.D. Thesis, University of Leeds, U.K., 2007.
17. Rosam J, Jimack PK, Mullis AM. A fully implicit, fully adaptive time and space discretisation method for phase-field simulation of binary alloy solidification. Journal of Computational Physics 2007; 225:1271-1285.
18. Bank RE, Jimack PK. A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations. Concurrency and Computation: Practice & Experience 2001; 13:327-350.