An efficient fully discrete scheme with unconditional energy stability and second-order temporal accuracy for the time-fractional Navier–Stokes equations with nonlinear damping

This paper proposes an efficient fully discrete scheme for solving time-fractional Navier–Stokes equations with nonlinear damping. The time discretization employs a non-uniform L2-1 σ approach, while the spatial discretization uses the Fourier spectral method. Theoretically, we prove the unconditional energy stability of the proposed scheme and establish a convergence estimate. Numerically, some numerical experiments are conducted to test the theoretical results, which illustrate the accuracy and effectiveness of the proposed scheme.