Parallelization and scalability issues of a multilevel elastohydrodynamic lubrication solver

Goodyer, Christopher E.; Berzins, Martin

doi:10.1002/cpe.1103

Cited by 17 publications

(29 citation statements)

References 28 publications

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“…Parallel implementation of the solver is achieved via a geometric decomposition of the computational domain, based on a partitioning strategy of the coarsest grid used. Its basic philosophy follows that employed in [12] and is described in greater detail in [10].…”

Section: Methods Of Solutionmentioning

confidence: 99%

Droplet migration: Quantitative comparisons with experiment

Koh

Lee

Gaskell

et al. 2009

Eur. Phys. J. Spec. Top.

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Abstract. An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H * , of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H * be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H * near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H * and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.

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Section: Methods Of Solutionmentioning

confidence: 99%

Droplet migration: Quantitative comparisons with experiment

Koh

Lee

Gaskell

et al. 2009

Eur. Phys. J. Spec. Top.

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“…A most commonly used method to calculate the elastic deformation of the surfaces is based upon evaluation of an elastic deformation integral [13,19,29,42,43] which is obtained by an analytical solution of the linear elasticity equation on a semi-infinite domain. A number of efficient numerical techniques have been developed over the past few decades using this half-space approach, for example the multilevel multi-integration (MLMI) method [9].…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

Ahmed

Goodyer

Jimack

2014

Computer Methods in Applied Mechanics and Engineering

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This paper presents an automatic locally adaptive finite element solver for the fullycoupled EHL point contact problems. The proposed algorithm uses a posteriori error estimation in the stress in order to control adaptivity in both the elasticity and the lubrication domains. The implementation is based on the fact that the solution of the linear elasticity equation exhibits large variations close to the the fluid domain on which the Reynolds equation is solved. Thus the local refinement in such region not only improves the accuracy of the elastic deformation solution significantly but also yield an improved accuracy in the pressure profile due to increase in the spatial resolution of fluid domain. Thus, the improved traction boundary conditions leads to even better approximation of the elastic deformation. Hence, a simple and an effective way to develop an adaptive procedure for the fully-coupled EHL problem is to apply the local refinement to the linear elasticity mesh. The proposed algorithm also seeks to improve the quality of refined meshes to ensure the best overall accuracy. It is shown that the adaptive procedure effectively refines the elements in the region(s) showing the largest local error in their solution, and reduces the overall error with optimal computational cost for a variety of EHL cases. Specifically, the computational cost of proposed adaptive algorithm is shown to be linear with respect to problem size as the number of refinement levels grows.

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“…The parallel implementation undertaken here follows [15] in its basic philosophy. In particular, the parallelism is achieved via a geometric decomposition of the domain, which is based upon a partition of the coarsest grid.…”

Section: Numerical Methods and Parallel Solution Proceduresmentioning

confidence: 99%

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

Gaskell¹,

Jimack²,

Koh³

et al. 2008

Numerical Methods in Fluids

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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.

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Parallelization and scalability issues of a multilevel elastohydrodynamic lubrication solver

Cited by 17 publications

References 28 publications

Droplet migration: Quantitative comparisons with experiment

Droplet migration: Quantitative comparisons with experiment

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

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

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