求解不可压缩Navier-Stokes方程的两层水平方法研究

Navier-Stokes equations are wildly applied in weather forecasting, oilfield development simulation，environmental pollution prognosis, artificial organ and so on. The project is focused on the two-level methods for the Navier-Stokes equations and their application as well as implementation. The main contents include：.1. Research the two-level methods based on operator splitting schema and nonlinear iteration formula;.2. Construct some novel unified stabilized two-level finite element methods for the Navier-Stokes equations and analyze their error estimate; .3.Present the high accuracy p-version two-level for solving the Navier-Stokes equations. Through this project, we will get a number of novel high efficiency numerical algorithms for solving the Navier-Stokes equations. .Furthermore, we give numerical simulation for the coupled Navier-Stokes problems to show the efficiency of the proposed algorithm. Finally，we implement the corresponding algorithms through C++ Language by object-oriented technique and modularization programming method in order to give more numerical simulations of the fluid dynamics..

Navier-Stokes方程在气象预报、油田开发的动态模拟、环境污染预报、人工脏器的流体力学问题模拟等学科中有广泛的应用。本项目主要研究求解Navier-Stokes方程两层水平的算法构造与实现。其主要内容包括：1.基于算子分裂与非线性迭代的新型两层水平方法构造与实现；2.带稳定项的两层水平有限元方法构造与误差分析；3.研究高精度p-形式的两层水平方法求Navier-Stokes方程。通过本项目，我们获得一些新颖高效率的求解Navier-Stokes方程的数值算法。在此基础上，对其型进行数值模拟，从而验证算法的高效性。此外，我们通过C++语言进行模块化程序设计给予相应算法实现，以便应用于更多流体力学问题的数值模拟。

Navier-Stokes方程在计算流体力学中有着广泛的应用。本项目主要研究求解Navier-Stokes方程两层水平（多层水平）的算法构造与实现。通过一年的努力.与工作，本课题的研究工作进入结题工作。在本项目的资助下，主要有以下成果： .(1)发表sci文章1篇，收录1篇，正在审稿2篇；.(2)求解Navier-Stokes方程的Matlab程序包一个；.(3)参加国内学术一次。.通过本项目，我们获得了一些新颖高效率的求解偏微分方程的两层水平、多层水平算法数值算法。在此基础上，我们利用Matlab实现相应算法，并应用于其他重要偏微分方程问题的数值模拟。