弹性流体动力润滑（EHL）问题的并行计算机全变差递减（TVD）方法
Total Variation Diminishing (TVD) method for Elastohydrodynamic Lubrication (EHL) problem on Parallel Computers
摘要：
在本文中，我们提供了一种新的数值方法，用于解决弹流润滑线和点接触问题，使用一类全变差递减（TVD）格式在并行计算机上。提出了一种求解离散变分不等式的投影交错象限互锁因子分解（PAQIF）的直接并行方法。对于一维弹流问题，我们利用Newton-Raphson近似中的加权变换，在整个计算域上划分两个子域，以带状矩阵的形式计算雅可比矩阵。通过测量感兴趣区域上的扩散系数和离散网格长度的比率来组装这样的子区域矩阵。然后将带状矩阵处理到并行计算机上，用PAQIF算法求解离散线性互补系统。通过在x和y方向上分别进行适当的分裂，该思想很容易推广到二维弹流润滑情况。在串行和并行计算机上进行了数值实验和分析，以验证计算解的性能。
英文摘要：
In this article, we offer a novel numerical approach for the solution of elastohydrodynamic lubrication line and point contact problems using a class of total variation diminishing (TVD) schemes on parallel computers. A direct parallel approach is presented by introducing a novel solver named as projected alternate quadrant interlocking factorization (PAQIF) by solving discrete variational inequality. For one-dimensional EHL case, we use weighted change in Newton-Raphson approximation to compute the Jacobian matrix in the form of a banded matrix by dividing two subregions on the whole computation domain. Such subregion matrices are assembled by measuring the ratio of diffusive coefficient and discrete grid length on the domain of the interest. The banded matrix is then processed to parallel computers for solving discrete linearized complementarity system using PAQIF algorithm. The idea is easily extended in two-dimensional EHL case by taking appropriate splitting in x and y alternating directions respectively. Numerical experiments are performed and analyzed to validate the performance of computed solution on serial and parallel computers.
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