Efficient Numerical Methods for Viscous Incompressible Flows

粘性不可压缩流的高效数值方法

• 批准号: 0512176
• 负责人: Jian-Guo Liu
• 金额: $ 28.34万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0512176&HistoricalAwards=false
• 关键词: Efficient; Numerical; Methods; Viscous; Incompressible

The investigator develops a class of efficient and accurate numericalmethods for the unsteady viscous incompressible Navier-Stokesequations (NSE) based a new unconstrained formulation of NSE withfully dissipation in contrast to the traditional formulation where theStokes operator is dissipative only in the divergence freefields. This class of NSE solver is unconditionally stable withexplicit treatment of both pressure and convection terms. Moreover, inthis class of finite element methods, there is no requirement of theso called inf-sup condition. The cost of solving NSE is greatlyreduced to solving a standard heat equation and a standard Poissonequation at each time step for general three dimensional fluid problems.The simplicity of the method also enable the PI to develop a class ofnumerical methods for complex fluids such as magneto-hydrodynamics,liquid crystal polymers, geodynamo, climate modeling, and large eddyturbulence simulations;Computational Fluid Dynamics has grown from a mathematical curiosityto become an essential tool in almost every branch of fluid dynamics,from aerospace propulsion to weather prediction and has receivedextensive attention throughout the international community since theadvent of the digital computer. The accuracy and efficiency of theproposed schemes will allow us to simulate general three-dimensionaltime-dependent flows with a reasonable turn-over time. It is expectedthat the proposed fast algorithms will become an important tool formany scientists and engineers in numerous scientific and industrialapplications of current interest.

研究人员为不稳定的粘性粘性不可压缩的Navier-Stokesequations（NSE）开发了一类高效，准确的数值方法，基于新的NSE的新型NSE的新配方与传统配方相反，与传统的配方相比，TheStokes Operator仅在Divergerence Freefields中散发出差异性。这类NSE求解器无条件地稳定，对压力和对流术语都有明确的处理。此外，在这类有限元方法中，不需要这种称为INF-SUP条件。解决NSE的成本是为了解决标准的热方程式和标准poissonequation的总体评估，以便在每个时间步骤中用于一般三维流体问题。流体动力学，液晶聚合物，地球瘤，气候建模和大型涡受扰动模拟；计算流体动力学已经从数学好奇心开始增长，几乎成为流体动力学的每个分支，从航空航天推进到天气预测，并在整个国际上都受到了国际关注社区以来数字计算机的Theadvent。 该方案的准确性和效率将使我们能够以合理的转换时间模拟一般的三维依赖性流动。 预计拟议的快速算法将成为当前兴趣的许多科学和工业应用中的重要工具科学家和工程师。