Transient EHD calculations have moved to the center of the attention in the past years as more machine elements that operate under variable operating conditions, such as automotive engine components, are examined. Almost all of the transient calculations today are carried out with a constant time step using first or second order discretisation for the determination of the time derivatives. Recently, a method was proposed that could control the time stepping of a transient calculation using first order time derivatives. In this paper, a method is presented for the control of the time step in transient calculations. The method employs a second order backward differentiation scheme with variable time stepping for the determination of the time derivatives. The time interval between successive calculations is determined depending on an estimate of the local truncation error without solving additional large linear systems, thus allowing for larger time steps when the time derivative is almost constant. This time stepping control method was implemented in an EHD simulation code that employed multi-grid and multi-level multi-summation techniques. Results presented in this paper prove that the proposed method can significantly reduce the number of necessary time steps of a transient calculation without any loss of accuracy of the results.
Variable Timestepping in EHD Problems
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Bakolas, V, & Borchers, W. "Variable Timestepping in EHD Problems." Proceedings of the World Tribology Congress III. World Tribology Congress III, Volume 1. Washington, D.C., USA. September 12–16, 2005. pp. 435-436. ASME. https://doi.org/10.1115/WTC2005-63116
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