分数阶Oldroyd-B黏弹性Poiseuille流的Laplace数值反演分析

采用Laplace数值反演的Stehfest算法研究了分数阶Oldroyd-B粘弹性流体在两平板间非定常的Poiseuille流动问题.首先,通过数值解与近似解析解的比较验证了Stehfest算法的有效性.其次,运用Stehfest算法对平板Poiseuille流动进行了研究,揭示了分数阶黏弹性平板流的速度过冲和应力过冲现象,指出这些现象对分数导数的阶数存在明显的依赖性.同时,数值结果表明,整数阶本构方程仅仅是分数阶本构方程的特例,分数阶本构方程较整数阶本构方程具有更广泛的适用性.

Analysis on fractional Oldroyd-B viscoelastic Poiseuille flow by numerical inversion of Laplace transforms

In this paper the unsteady Poiseuille flow of fractional Oldroyd-B viscoelastics fluid between two parallel plates is studied, which sheds light on the investigation on fractional differential equations. Stehfest algorithm for numerical inversion of Laplace transform is used for obtaining the numerical solutions, and its validity is verified by comparing the results with approximate analytic solutions. Then the laminar Poiseuille flow of fractional Oldroyd-B viscoelastic fluid is investigated by the Stehfest algorithm. Phenomena of velocity and stress overshootings are found, which are proved to be dependent on the order of fractional derivative. Simultaneously, compared with the integer constitutive equations, the fractional constitutive equations have wider scope of application. This conclusion was drawn based on the obvious fact that the integer constitutive equations are only special cases of the fractional constitutive equations.