线接触弹流润滑问题的贴体坐标变换和交错网格解法

Body fitted coordinate transformation and staggered grid method for the solution of EHL line contact problem

通过贴体坐标变换把带自由边界的线接触弹流润滑问题化为定边界问题．在分析了目前常用解法的二阶格式失隐（因而不得不采用一阶格式）的原因后，提出了一种交错网格上的二阶格式．算例表明，本二阶格式不仅比一阶格式的精度有显著提高，而且具有良好的数值稳定性．

he EHL line contact problem with free boundary is tranformed into a fixed boundary problem by body fitted coordinate transformation,which makes the solution procedure much simpler and. the computational amounts much reduced. A second order scheme on a staggered grid for the solution of EHL line contact problem is proposted and the resultant nonlinear algebraic equations are solved by Newton-Raphson iterations. The numerical examples show that the proposed second order scheme not only has much higher accuracy than the first order scheme which is widely used currently,but also has good numerical stability even in very high load. It is found in this paper that compared with the discretization of film thickness equation,the discretization of fluid dynamic equation is of dominant importance to accuracy and numerical stability of numerical solution of EHL problem.