Numerical analysis of fractional viscoelastic fluid problem solved by finite difference scheme

The finite difference schemes for equations depicting the fluid flow, heat and mass transfer of viscoelastic fluid in porous media based on fractional constitutive model are analyzed, when Soret and Dufour effects are taken into account. Different from the conventional fractional partial differential equations, the governing momentum equation of this system not only contains convection terms, but also a term: 0Dt beta(??(2)??/????(2)), which are great challenges when we do the stability analysis. In addition, the temperature equation and concentration equation are coupled with each other, which increases the difficulty of numerical analysis. By using the energy method, the stability and convergence of the finite difference schemes employed for the governing equations are obtained. The accuracy of the scheme for momentum equation is O(??(2) + h(x)(2)+ h(y)(2)), while the one for temperature and concentration equations is O(??(2) + h(x)(2)+ h(y)). Finally, numerical examples are presented to verify methods and demonstrate the analysis effectiveness.