Jacobi spectral collocation method of space-fractional Navier-Stokes equations

Abstract

In this paper, we study the Jacobi spectral collocation method for two-dimensional space-fractional Navier-Stokes equations with Laplacian and fractional Laplacian. We first derive modified fractional differentiation matrices to accommodate the singularity in two dimensions and verify the boundedness of its spectral radius. Next, we construct a fully discrete scheme for the space-fractional Navier-Stokes equations, combined with the first-order implicit-explicit Euler time-stepping scheme at the Jacobi-Gauss-Lobatto collocation points. Through some two-dimensional numerical examples, we present the influence of different parameters in the equations on numerical errors. Various numerical examples verify the effectiveness of our method and suggest the smoothness of the solution for further regularity analysis.