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：雷诺方程结合考虑空化效应的埃尔罗德算法后，形式上类似于非线性对流-扩散-反应方程。采用有限元法求解时，在对流主导区域（即空化发生区域）易产生数值振荡。本文基于变分多尺度方法提出一种稳定化有限元方案，通过引入正交子网格尺度概念，仅需在弱形式中添加一个附加项即可获得稳定算法，且网格加密时具有最优收敛性。