Analysis of the absorbing boundary condition for the Maxwell fluid flow over a semi-infinite plate with considering the magnetic field

Abstract

In this paper, we analyze the flow mechanism of the Maxwell fluid over a semi-infinite plate. To handle the semi-infinite boundary, the artificial boundary method is employed and the absorbing boundary condition in the form of convolution is derived. Besides, the stability of the absorbing boundary condition is analyzed. Solutions are obtained numerically using the finite difference method and the accuracy is verified by introducing a source term to construct the exact solution. To demonstrate the validity and reasonableness of the absorbing boundary condition, a comparison with the direct truncation boundary is discussed. Our study examines the effects of the magnetic field, relaxation parameter, oscillation frequency and plate amplitude on the velocity distribution and flow mechanism of the Maxwell fluid.