Jacobi Spectral Allocation Method For Spatial Fractional Navier-Stokes Equations

Spectral method has developed rapidly in recent decades because of its high-precision.In this thesis,we study Jacobi spectral collocation method for two-dimensional space fractional Navier-Stokes equations.Firstly,in order to eliminate the singularity in the integral kernel of Riemann-Liouville fractional derivative,we give the modified left and right Riemann-Liouville fractional pseudospectral differential operators,and derive the modified left and right RiemannLiouville fractional pseudospectral differential matrices.Then,we give the detailed derivation process of pseudospectral differential matrix of Riesz type fractional Laplacian operator on two-dimensional collocation points,and verify the boundedness of its spectral radius.Next,we construct a fully discrete scheme for the space fractional Navier-Stokes equations,which is combined with the first-order implicit-explicit Euler time-stepping scheme at the Jacobi-GaussLobatto collocation points.Through some two-dimensional and three-dimensional numerical examples,we present the influence of different parameters in the equations on numerical errors.Rich numerical examples verify the effectiveness of our method.