An Explicit Method for Numerical Solution of the Equation Governing the Motion of a Particle Under Arbitrary Force Fields

Subject Areas : International Journal of Mathematical Modelling & Computations

Ghiyam Eslami ¹ , Masoumeh Zeinali ²

1 - Department of Mechanical engineering, Islamic Azad University, Ahar Branch, Ahar, Iran
2 - Faculty of mathematics, statistics and computer sciences, University of Tabriz,Tabriz, Iran

Received: 2023-06-23 Accepted : 2023-08-10 Published : 2023-09-17

Keywords: Numerical Solution, Integro-differential equation, Particle motion, Basset history force, Creeping flow,

Abstract :

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.