The Oscillatory Flow of Oldroyd-B Fluid with Magnetic Disturbance

Abstract

The magnetic field intensity will be nondeterminacy with the flow of charged particles thrown out by solar activities, the overlap of adjacent magnetic islands or non-axisymmetric magnetic interference in tokamaks and so on. The model of a generalized Oldroyd-B fluid with fractional derivative under oscillating pressure gradient and magnetic field with some disturbance will be considered in this paper. The disturbance is regarded as the background noise of the system, and the model is described by a fractional stochastic differential equation. Time and space are discretized by L1, L2 schemes based on piecewise linear interpolation and the central difference quotient method. We demonstrate the effects of the amplitude and period of the oscillating pressure gradient, magnetic parameter, fractional parameters and noise on the velocity field, and two special cases are given.

Keywords

• Oldroyd-B fluid
• fractional stochastic differential equation
• oscillating pressure gradient
• numerical method