关于N-S方程惯性流形算法的研究

The theory research and numerical computation of Tuburlence is very important in the nonlinear science and industry application. This project studies the existence,the upper bound of the Hausdorff and Fractal dimemsion of the attractor and numerical methods for the N-S equations and the relative MHD equations describing the turblence. By applying the theory of the infinit.dimensional dynamic system and Inretial manifold, we design the nonlinear Galerkin method, coupling finite element and boundary element nonlinear Galerkin method and postprocessing Galerkin method which can help us to know and describe the turblence of the interior flow and exterior flow.

对湍流的认识及数值模拟能力，在非线性科学和工业应用中具有非常重要意义。本课题对非定常Ｎ－Ｓ方程内外部问题研究其奇异点集和吸引子的数学结构及一些有效算法。通过应用无穷维动力系统理论及惯性流形、区域分裂、多层算法、有限元边界元耦合算法、后处理Ｇａｌｅｒｋｉｎ方法等现代算法的研究，可望对三维真实流动中湍流的机理和特性有更好的数学描述。