论文标题
平行计算机上的弹性流体动力润滑（EHL）问题的总变化减少（TVD）方法
Total Variation Diminishing (TVD) method for Elastohydrodynamic Lubrication (EHL) problem on Parallel Computers
论文作者
论文摘要
在本文中，我们提供了一种新颖的数值方法，用于使用平行计算机上的一类总变化（TVD）方案解决弹性流体动力润滑线和点接触问题。通过引入一个称为投影交替的象限互锁分解（PAQIF）的新颖求解器来提出直接平行方法，通过求解离散的变异不平等。对于一维EHL情况，我们使用牛顿 - 拉夫森近似中的加权变化来计算带有带矩阵的形式的雅各布矩阵，通过在整个计算域上划分两个子区域。通过测量利益域对扩散系数和离散网格长度的比率来组装此类矩阵。然后将带状矩阵处理到并行计算机，以使用PAQIF算法求解离散的线性互补系统。通过分别在X和y交替的方向上进行适当的分裂，可以在二维EHL情况下很容易扩展这个想法。进行数值实验和分析，以验证在串行和并行计算机上计算的解决方案的性能。
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.
