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.

该项目将基于纳维-斯托克斯方程的重新表述，开发一类新颖且非常有效的不可压缩流数值方法，该方程已被证明是适定的，并为涡度方面的粘性对压力的贡献提供了边界条件循环。 主要见解是，边界涡度的总产生可以通过拉普拉斯算子和亥姆霍兹投影算子之间的换向器来精确计算。此外，该项由粘度项主导，因此我们可以明确地处理它以获得效率和稳定性。主要优点是该方法可以在标准连续有限元空间中表述，并且不需要速度和压力近似空间的兼容性条件。因此，标准快速求解器可以直接应用于纳维-斯托克斯方程。复杂域中3D流动的精确、高效模拟仍然是许多科学和工程问题的主要挑战。物理边界附近流动的分辨率对于准确预测升力和阻力、涡流脱落和边界层分离等体积力至关重要。该项目的成功将对科学和工程的许多分支产生重要影响。它将提供更准确的体积力预测，从而为交通相关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。