高雷诺数不可压缩流动是常见的流动现象。本项目拟构造出一种数值模拟高雷诺数不可压缩流动的参数自适应的新型有限元变分多尺度方法，该方法基于有限元插值多项式的阶数实现流场尺度分离，在计算非线性的定常Navier-Stokes方程过程中，适时调整稳定化参数的取值，以快速高效地获得高精度的有限元解。同时分别设计出基于两重网格离散和完全重叠型区域分解的参数自适应的并行变分多尺度算法，前者首先在一粗网格上用参数自适应的新型变分多尺度方法求解Navier-Stokes方程，然后在细网格的子区域上并行求解相应的残差方程以校正粗网格的解；后者每台处理器在一局部加密的全局网格上使用参数自适应的变分多尺度方法相互独立地求解各自子区域的局部有限元解。使用有限元局部误差估计、区域分解、变分多尺度及两重网格方法的理论工具，我们将对算法进行数值分析，同时给出并行数值模拟结果，为计算流体力学在工业部门中的应用提供参考。

High Reynolds number incompressible flows are common flow phenomena in real world. This project aims to develop a new parameter-self-adaptive finite element variational multiscale method for simualtion of high Reynolds number incompressible flows. The scale-separation of the flow in this method is implemented via interpolation of polynomials of different orders for finite element discretization. During the solution process of the stabilized nonlinear steady Navier-Stokes equations,the stabilization parameter is adjusted in time to quickly obatin the finite element solution with high accuracy. At the same time, we will develop two classes of parallel parameter-self-adaptive finite element variational multiscale algorithms based on two-grid discretization and fully overlapping domain decomposition, respectively. In the former class of parallel algorithms, we first solve the Navier-Stokes equations on a coarse grid by the developed new parameter-self-adaptive finite element variational multiscale method, and then correct the solution by solving the resultant residual equations on fine grid subdomains in a parallel manner; while in the later class of parallel algorithms, each processor independently computes a local solution in its own subdomain on a locally refined gobal grid by using the developed new parameter-self-adaptive finite element variational multiscale method. By the technical tools of local error estimates for finite element solution, domain decomposition methods, variational multiscale methods and two-grid method, we will theoretically analyze the developed algorithms, and give numerical results to provide references for the applications of computational fluid dynamics in industry.