Coupled lubrication and Stokes flow finite elements

Abstract

SUMMARYA method is developed for performing a local reduction of the governing physics for uid problems with domains that contain a combination of narrow and non-narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the uid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two-dimensional Navier-Stokes equations to the one-dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non-narrow region with boundary conditions on the mass and momentum ux. The localized reduction technique, termed 'stitching,' is demonstrated on Stokes ow for various geometries of the hydrodynamic journal bearing-a non-trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes-Reynolds method is illustrated on an industrially applicable fullyooded deformable-roll coating example. The examples in this paper are limited to two-dimensional Stokes ow, but extension to three-dimensional and Navier-Stokes ow is possible.

Multiscale modelling in the numerical computation of isothermal non-wetting

“…The use of overlapping domains and the implementation of boundary conditions through a variation of the domain-decomposition Schwarz alternating method enabled hybrid solutions to be obtained. Stay & Barocas (2003) applied a Galerkin finite-element technique to compute Stokes flow in the vicinity of a thin region and coupled the results to a lubrication solution in the thin region. The technique was illustrated with a deformable roll-coating geometry.…”

Dynamic wetting failure in surfactant solutions

“…The model is evaluated using three approaches: (i) a one-dimensional (1D) lubrication-type approach, (ii) a novel hybrid of a 1D description of the receding phase and a 2D description of the advancing phase, and (iii) an asymptotic theory of Cox (1986b). Although similar 1D/2D hybrid approaches have previously been used to study single-phase (Stay & Barocas 2003) and two-phase (Smith & Neitzel 2006;Lavalle et al 2015) flows, this is the first work, to the best of the authors' knowledge, that presents a hybrid model for fluid displacement with dynamic contact lines.…”

On the efficiency and quality of numerical solutions in CFD problems using the interface strip preconditioner for domain decomposition methods

“…Triggered by observed discrepancies between experimental results and computer simulations [25] using standard solvers [26] (i.e. GMRes with acceptable rates of convergence), this example shows the improvement of the solution of lubricated contacts by means of the ISP preconditioner.…”