A new numerical scheme for non uniform homogenized problems: application to the nonlinear Reynolds compressible equation.
type: Item
instance of: scholarly article
title: A new numerical scheme for non uniform homogenized problems: application to the nonlinear Reynolds compressible equation.
zbMATH Open document ID: 1112.76433
DOI: 10.1155/S1024123X01001685
author: Gustavo C. Buscaglia
author: Mohammed Jai
published in: Mathematical Problems in Engineering
publication date: 2002-10-31T00:00:00Z
full work available at URL: https://eudml.org/doc/53113
review text: Summary: A new numerical approach is proposed to alleviate the computational cost of solving nonlinear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost. The overall efficiency of the numerical methodology makes it feasible to apply rigorous homogenization techniques in the analysis of compressible fluid contact considering roughness effects. Previous work makes use of an heuristic averaging technique. Numerical comparison proves that homogenization-based methods are superior when the roughness is strongly anisotropic and not aligned with the flow direction.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76M50
Mathematics Subject Classification ID: 76D08
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 1790998
zbMATH Keywords: Compressible Reynolds lubrication equation
zbMATH Keywords: Taylor expansions
zbMATH Keywords: Numerical homogenized problems.
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1790998