针对不可压粘性流动与导热问题，我们研究基于投影方法的修正特征有限元方法。利用投影方法，把非定常Navier-Stokes方程或流体热动力学方程组分解为几个抛物和椭圆方程，对抛物方程利用特征方法对时间导数项和对流项进行离散，而空间离散利用已有的空间离散方法——有限元方法或有限体积方法。我们将给出数值格式的稳定性分析和误差估计，给出数值计算实验，并把数值实验结果和已有的结果进行比较分析，从而给出若干稳定性好、适应性强、收敛的高精度格式。对大雷诺数流动进行长时间的数值模拟，以研究解的渐进性行为，为研究湍流发展的行为和机理以及数值模拟湍流提供可靠的理论依据和算法工具。从而，也更清楚地认识非线性流动的本质，为非线性科学研究提供新的研究工具，也能为计算流体力学在工程中的应用提供新的工具和理论。

In this progrem,we studied the modified characteristics projection finite element method of the incompressible viscous flow and heat tranfer. Using projection method, the unsteady Navier-Stokes equation or fluid thermodynamic equation is decomposed into several parabolic and elliptic equations, time derivative and convective terms of the parabolic equation are discretized by the characteristics method, while the spatial is discretized by the finite element method or finite volume method. We will give the stability analysis and error estimate, numerical experiments are also given, and the numerical results will be compared with the existing numerical results. In this way, we will give several stability, robustness and high convergence precision numerical methods. In order to study the long time behavior of the solutions, behavior and the mechanism of development of turbulence flow and provide a reliable theoretical basis and algorithm tools for the numerical simulation of turbulent flow, we will give the numerical results of the high Reynolds number flow in long time.Thus, we will understand the nature of nonlinear flow more clearly, provide new research tools for the non-linear science, and give new tools and theories for the computational fluid dynamics in the engineering.