Economic Difference Methods of High Accuracy for Solution of the Time Dependent, Gas-Lubrication Equation

摘要

The Reynolds equation provides an accurate description of the pressure distribution in a gas bearing, but it is very nonlinear, and solution is quite difficult. The importance of solving Reynolds equation to the understanding and design of gas bearings has led to recent emphasis on numerical techniques. Previous methods for practical bearing configurations, both for steady-state problems requiring a fine mesh and for dynamic problems in general, have been time consuming. This paper presents economic, stable, and highly accurate difference methods of solving these problems - economic in the sense of rapid execution per time step (O(MN) operations required on an MxN mesh) - and highly accurate in that the temporal truncation error is O(delta T squared). An alternating direction implicit technique is used to induce locally one-dimensional difference approximations to the Reynolds equation, and this is combined with an extrapolated Crank-Nicolson scheme to obtain the high temporal accuracy. Economic versions of the standard implicit methods are also developed. The finite length partial arc bearing is used to compare the new schemes to the standard methods used in gas bearing numerical work (explicit, implicit, and semi-implicit schemes). Extensive comparisons show the efficacy and accuracy of the new techniques in both steady-state and transient calculations. (Author)