不可压缩流动因其普遍性、基础性和工程重要性，在流体力学中处于中心地位。数值求解大雷诺数流动问题存在非线性、对流占优、数值耗散和算法稳定性等诸多难点。项目拟结合变分多尺度和两重网格方法及单位分解，发展一类局部并行算法及其局部自适应算法。项目主要思想是在全局粗网格上求解变分多尺度模型，得到全局低频分量，再在局部区域的细网格上求解一系列相互独立的线性化变分多尺度残量子问题，捕捉到解的高频信息，并利用局部后验误差估计子对局部区域和子问题进行自适应加密和求解，最后基于单位分解构造具有全局连续性的整体解。该类算法采用变分多尺度方法降低直接数值模拟对计算网格的苛刻要求，同时使用基于单位分解和两重网格的局部并行方法，控制局部人工能量耗散、降低子区域间的并行信息通讯和求解规模。项目的顺利实施将丰富变分多尺度方法和局部并行算法的研究内容，为不可压缩流动问题的大规模数值仿真提供一类算法基础和理论支持。

The incompressible flow plays a leading centre due to its universality, fundamentality and engineering importance. Numerical simulations of such flows with large Reynolds numbers face on many challenging problems, such as the nonlinearity, convection domination, numerical dissipation and stability of the algorithm provided. This program will combine the methods of variational multiscale method(VMS) and two-grid and the technique of the partition of unity, and develop a class of the local and parallel algorithms and the related local adaptive algorithms. The main idea of the program lays on that, firstly the variational multiscale model is computed on a global coarse grid to obtain the global lower frequency approximation; then a series of mutually independent linearized variational multiscale residual sub-problems in the local sub-domains are solved on some finer meshes in parallel to capture the higher frequency components, meanwhile the local posteriori error estimators are used to refine the local sub-domains for the local sub-problems; finally the partition of unity is applied to construct the globally continuous finite element solutions. These algorithms can reduce the requirements required by direct numerical simulation(DNS) by using VMS in one aspect, and also control the local artificial energy dissipation, require less parallel communication between sub-domains, and reduce the scales of the sub-problems in another aspect. The successfully implement of the program will enrich the research fields of the VMS and local and parallel algorithms, and provide a class of basic algorithms and theorical supports in large scale numerical simulations for solving the incompressible flows.