Insight into the significance of absorbing boundary condition for the flow mechanism analysis of fractional Maxwell fluid over a semi-infinite plate

Abstract

Viscoelastic fluids have many applications in engineering, and studying the complex fluidity of viscoelastic fluids can improve their applicability. Based on the flow caused by the pressure or the moving plate with various velocities, the aim of this paper is to deeply study the significance of absorbing boundary condition for the flow mechanism analysis of the fractional Maxwell fluid, of which the constitutive relation is formulated by introducing the relaxation parameter and the fractional parameter with considering the memory characteristics. For treating the model in a semi-infinite boundary domain, the artificial boundary method is applied to transfer it to a problem in a bounded domain with absorbing boundary condition, which is solved numerically by the finite difference method combined with the L1 formula and verified by numerical examples. The difference of the flow characteristics is subject to the direct truncation boundary condition and the absorbing boundary condition is compared and the effectiveness and rationality are analyzed graphically, and the influences of the dynamic parameters on the velocity and the flow mechanism are also discussed. The main findings of this research are that the larger relaxation parameter plays a role in a stronger delay effect, a larger fractional parameter refers to the stronger memory characteristics of the delay effect, and the smaller Reynolds number leads to the larger viscous force, all of which lead to a slower flow process.