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

Abstract

SUMMARYWe consider the parallel application of an efficient solver developed for the accurate solution of a range of droplet spreading flows modelled as a coupled set of nonlinear lubrication equations. The underlying numerical scheme is based upon a second-order finite difference discretization in space and a secondorder, fully implicit, adaptive scheme in time. At each time step, this leads to the need to solve a large system of nonlinear algebraic equations, for which the full approximation storage multigrid algorithm is employed. The motion of the contact line between the three phases (liquid, air and the solid substrate) is based upon the assumption of a thin precursor film, with a corresponding disjoining pressure term in the governing equations. It is the inclusion of this precursor film in the model that motivates the need for a parallel solution method. This is because the thickness of such a film must be very small in order to yield realistic predictions, while the finite difference grid must be correspondingly fine in order to obtain accurate numerical solutions. Results are presented which demonstrate that the parallel implementation is sufficiently efficient and robust to allow reliable numerical solutions to be obtained for a level of mesh resolution that is an order of magnitude finer than is possible using a single processor.

Reliable performance prediction for multigrid software on distributed memory systems

“…As described in the introduction, this is an extremely important class of numerical algorithm which, due to its computational efficiency, is becoming more and more widely used in practical engineering software. Illustrative work includes [9,[11][12][13]16,19,20,28], but there are many more examples that could be cited. The original multigrid approach, e.g.…”

“…In particular we consider heterogeneous and multicore processor architectures, combined with different communication architectures, such as Myrinet and Fast Ethernet switching. Furthermore, unlike our previously published work [23][24][25]27], we demonstrate the effectiveness of our approach on practical engineering software [12,13], in addition to codes that are based upon slightly less complex mathematical models [11].…”

“…[3,[11][12][13]19]. This is typically based upon using a geometric partition of the coarsest mesh that is present and then mapping this in the natural manner to each of the finer meshes.…”

Modelling the Flow of Droplets of Bio-Pesticide on Foliage

“…Examples include flow over homogeneous substrates with, Schwartz et al (2001), and without, Glass et al (2010), evaporation, with surfactants, Schwartz et al (2004) and for a non-Newtonian power-law liquid, Ahmed et al (2013), over heterogeneous substrates with variable wettability, Schwartz & Eley (1998) and containing in addition micro-scale topographical features, Gaskell et al (2004). A key challenge is achieving mesh independent solutions, Koh et al (2009), and spreading rates quantitatively comparable with those observed experimentally, Gaskell et al (2008).…”

“…Important examples are encountered in the deposition of coatings and inks, in enhanced oil recovery, the direct patterning of functional layers during microchip production and the cooling of electronic components, see for example Bear (1988); Gaskell et al (2008); Anandan & Ramalingam (2008).…”