Numerical solution of the time-fractional Navier–Stokes equations for incompressible flow in a lid-driven cavity

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This paper addresses a computational technique for solving 2D unsteady Navier–Stokes equations (NSEs) with time-fractional order in the Caputo sense in the formulation of stream function-vorticity. The finite difference-based method of lines is used to discretize the time-fractional NSEs on a collocated grid that construct a fractional differential algebraic equations system. After solving the discretized complementary Poisson’s equation, this system is reduced to a system of fractional differential equations (FDEs). The resulting FDEs are solved by fractional backward differentiation formulas. The flow in a square lid-driven cavity is considered as the model problem.