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In this paper, we consider the finite difference method for the generalizedtwo-dimensional (2D) multi-term time-fractional Oldroyd-B fluid model, which isa subclass of non-Newtonian fluids. Different from the general multi-term timefractional equations, the generalized fluid equation not only has a multi-termtime derivative but also possess a special time fractional operator on thespatial derivative. Firstly, a new discretization of the time fractionalderivative is given. And a vital lemma, which plays an important role in theproof of stability, is firstly proposed. Then the new finite difference schemeis constructed. Next, the unique solvability, unconditional stability, andconvergence of the proposed scheme are proved by the energy method. Numericalexamples are given to verify the numerical accuracy and efficiency of thenumerical scheme as compared to theoretical analysis, and this numerical methodcan be extended to solve other non-Newtonian fluid models.

Novel numerical analysis for simulating the generalized 2D multi-term time fractional Oldroyd-B fluid model