An explicit method for numerical solution of the equation governing the motion of a particle under arbitrary force fields

International Journal of Mathematical Modelling & Computations

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 دی 1402

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2024.1999587.1287

نویسندگان

Ghiyam Eslami^{* 1}؛ Masoumeh Zeinali²

¹Department of Mechanical engineering, Islamic Azad University, Ahar Branch, Ahar, Iran

²Faculty of mathematics, statistics and computer sciences, University of Tabriz,Tabriz, Iran

چکیده

In this paper, an implicit second order integro-differential equation governing unsteady motion of a solid particle submerged in a fluid medium and, affected by an arbitrary force field is solved numerically. It is assumed that the particle Reynolds number is quite small to use the well-known Basset kernel for the history force. The implicitness and singularity of the equation are removed by using a hybrid quadrature rule (HQR) and a generalized quadrature rule (GQR), respectively. A recursive plan is used to reduce the required CPU time. Two schemes along with the associated numerical solution algorithms are presented. It is described how the accuracy of the method can be increased in a systematic way. The results obtained by several examples show the effectiveness of the method.

کلیدواژه‌ها

Particle motion؛ Basset history force؛ Integro-differential equation؛ Creeping flow؛ Numerical solution