An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

作者：Ji, Cuicui; Sun, Zhizhong^*

来源：Numerical Mathematics: Theory, Methods and Applications , 2017, 10(3): 597-613.

DOI：10.4208/nmtma.2017.m1605

• Stokes' first problem
• heat flow
• fractional derivative
• finite difference scheme
• unconditional stability
• convergence

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes' first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Grunwald-Letnikov difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of rho(tau(2) + h(4)) in maximum norm, where tau and h are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

• 出版日期2017-8
• 单位东南大学