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.

翻译：雷诺方程结合埃尔罗德算法以包含空化效应后，其形式类似于非线性对流-扩散-反应方程。采用有限元求解时，在对流主导区域（空化发生时即存在该区域）容易产生数值振荡。我们提出一种基于变分多尺度方法的稳定化有限元方法，并利用正交亚网格尺度概念。研究表明，该方法仅需在弱形式中添加一项即可获得稳定算法，且在网格细化时能实现最优收敛性。