A Sparse Matrix-Based Method for Rapid Solving the Reynolds Equation

Abstract

Abstract Due to the repeated iteration, the numerical method represented by the finite-difference method has the disadvantages of low computational efficiency and long time-consuming in solving the Reynolds equation. This paper proposed a new sparse matrix-based method to solve the difference Reynolds equation by replacing the pressure iterative process with the sparse matrix solver. Compared with the traditional iterative methods, this new method's computational efficiency is about two orders of magnitude higher, and it shows high accuracy in different degrees-of-freedom. Two cases of aerostatic lubrication and elastohydrodynamic lubrication are used to illustrate the effectiveness of this method. This method can support the rapid analysis of fluid lubrication problems and lay the foundation for developing the lubrication calculation library.