Efficient Numerical Methods for Viscous Incompressible Flows

粘性不可压缩流的高效数值方法

• 批准号: 1011738
• 负责人: Jian-Guo Liu
• 金额: $ 12.12万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-11-18 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1011738&HistoricalAwards=false
• 关键词: Efficient; Numerical; Methods; Viscous; Incompressible

This project will address the development of a class of novel and very efficient numerical methods for incompressible flows based on a reformulation of the Navier-Stokes equations that has been proved well-posed and provides boundary conditions for the viscous contribution to pressure in terms of vorticity circulation. The main insight is that the total creation of boundary vorticity can be computed exactly by a commutator between the Laplacian and Helmholtzprojection operators. Moreover, this term is dominated by the viscosity term, hence we can treat it explicitly to gain efficiency and stability. The major advance is that the method can be formulated in standard continuous finite element space, and there is no compatibility condition needed for the velocity and pressure approximation spaces. Hence the standard fast solver can be applied to Navier-Stokes equation directly.Accurate, efficient simulations of 3D flows in complicated domain are still major challeges for many scientific and engineering problems. The resolution of the flows near physical boundaries is essential to the accurate prediction of the body force such as the lift and drag, shedding of vortex and boundary layer separation. The success of this project will have an important impact on many branches of science and engineering. It will give more accurate predictions of body force which will result in better energy efficiency for transportation related applications. It will provide fast and reliable simulations for scientific research and engineering application.

该项目将基于已被证明已被证明良好的Navier-Stokes方程的重新制定，以不可压缩的流量来开发一系列新颖且非常有效的数值方法，用于不可压缩的流量，并为涡流循环的压力施加粘性贡献提供了边界条件。 主要见解是，可以通过Laplacian和Helmholtzproctoction Operators之间的换向器来精确地计算边界涡度的总创建。此外，该术语以粘度项为主，因此我们可以明确对待它以提高效率和稳定性。主要的进步是该方法可以在标准的连续有限元元素空间中配制，并且速度和压力近似空间不需要兼容条件。因此，标准快速求解器可以直接应用于Navier-Stokes方程。对复杂域中的3D流进行有效的，有效的仿真仍然是许多科学和工程问题的主要Challeges。物理边界附近流量的分辨率对于准确预测体力的准确预测，例如升力和阻力，涡流和边界层分离。该项目的成功将对科学和工程的许多分支产生重要影响。它将提供对体力的更准确的预测，从而为相关的应用带来更好的能源效率。它将为科学研究和工程应用提供快速可靠的模拟。