Finite difference automatically generated non-uniform grids in the numerical solution of the Reynolds' compressible one-dimensional squeeze-film equation

Abstract

With the Reynolds equation, for compressible squeeze-film thrust bearings, the use of a finite difference discretization with a grid of nodes having a non-uniform spacing can result in a more efficient computation of the solution. Comparative tests of two variable spatial grid models against a uniform model were conducted with the classical finite difference methods for chosen combinations of squeeze number and excursion ratio values. For problems with a high value of σ, one of the non-uniform grid models has shown some advantages over the uniform model, requiring a smaller number of nodes and less computation time with the same solution accuracy.