基于丰富多尺度稳定化方法的Navier-Stokes方程有限体积迭代算法研究

In this paper, three finite volume iterative schemes for the steady incompressible Navier-Stokes equations are provided based on the multiscale enrichment method.Under different restriction on the viscosity parameter, the stability and convergence results of the considered numerical schemes are established. Theoretical findings show that the Stokes and Newton iterations are stable under some strong uniqueness conditions, while the Oseen iteration is unconditionally stable and convergent under the uniqueness condition. Furthermore, the Newton iteration is exponential convergence with respect to the iterative step. Numerical examples are presented to verify the established theoretical findings and show the performances of three iterative finite volume methods.