Numerical algorithm for two dimensional fractional Stokes' first problem for a heated generalized second grade fluid with smooth and non-smooth solution

摘要

In this paper, we consider the numerical solution of the two dimensional fractional Stokes' first problem for a heated generalized second grade fluid. The proposed method is based on the L1 finite difference scheme for the temporal direction while the Legendre spectral method for the spatial direction. Numerical stability and convergence of the method are rigorously established. At the mean time, the case of non-smooth solution is considered by adding some correction terms. Numerical experiments are included, which verify the theoretical predictions. (C) 2019 Elsevier Ltd. All rights reserved.