Stabilized finite elements for the solution of the Reynolds equation considering cavitation

TL;DR

This paper introduces a stabilized finite-element method based on the variational multiscale approach to accurately solve the Reynolds equation with cavitation effects, reducing oscillations in convection-dominated regions.

Contribution

It presents a novel stabilized finite-element technique that uses orthogonal subgrid scales to improve convergence and stability in cavitation modeling.

Findings

The method effectively reduces oscillations in convection-dominated regions.

It achieves optimal convergence with minimal additional computational complexity.

The approach is applicable to nonlinear convection-diffusion-reaction equations like the Reynolds equation.

Abstract

The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in convection-dominated regions, which are present whenever cavitation occurs. We propose a stabilized finite-element method that is based on the variational multiscale method and exploits the concept of orthogonal subgrid scales. We demonstrate that this approach only requires one additional term in the weak form to obtain a stable method that converges optimally when performing mesh refinement.