Efficient and accurate time adaptive multigrid simulations of droplet spreading

• Published in: International journal for numerical methods in fluids Vol. 45; no. 11; pp. 1161 - 1186
• Main Authors: Gaskell, P. H., Jimack, P. K., Sellier, M., Thompson, H. M.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.08.2004; Wiley
• Subjects: adaptive time-stepping; Computational methods in fluid dynamics; droplets; Drops and bubbles; Exact sciences and technology; Fluid dynamics; fully implicit; Fundamental areas of phenomenology (including applications); lubrication approximation; multigrid; Nonhomogeneous flows; Physics; spreading; Algorithms; Three dimensional flow; Computational fluid dynamics; Multigrid; Spreading; Digital simulation; Drops; Adaptive method
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.632

An efficient full approximation storage (FAS) Multigrid algorithm is used to solve a range of droplet spreading flows modelled as a coupled set of non‐linear lubrication equations. The algorithm is fully implicit and has embedded within it an adaptive time‐stepping scheme that enables the same to be optimized in a controlled manner subject to a specific error tolerance. The method is first validated against a range of analytical and existing numerical predictions commensurate with droplet spreading and then used to simulate a series of new, three‐dimensional flows consisting of droplet motion on substrates containing topographic and wetting heterogeneities. The latter are of particular interest and reveal how droplets can be made to spread preferentially on substrates owing to an interplay between different topographic and surface wetting characteristics. Copyright © 2004 John Wiley & Sons, Ltd.