This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition.ududThe roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods.
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机译：本文提出了一种新的数值方法来解决瞬态线接触弹性流体动力润滑（EHL）问题。高阶不连续Galerkin（DG）有限元方法用于空间离散化，标准Crank-Nicolson方法用于近似时间导数。 h适应性方法用于随时间变化的网格自适应，而惩罚方法用于处理空化条件。 ud ud此处使用的粗糙度模型是一个简单的压痕，位于上表面。数值结果将DG方法与标准有限差分（FD）技术进行了比较。结果表明，与使用低阶FD方法相比，微EHL特征的捕获自由度要少得多。
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