Mathematical Sciences: Efficient Numerical Methods for Large Reynolds Number Unsteady Viscous Incompressible Flows

数学科学：大雷诺数不稳定粘性不可压缩流的有效数值方法

• 批准号: 9505275
• 负责人: Jian-Guo Liu
• 金额: $ 5.81万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505275&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Efficient; Numerical; Methods

EFFICIENT NUMERICAL METHODS FOR LARGE REYNOLDS NUMBER UNSTEADY VISCOUS INCOMPRESSIBLE FLOWS Jian-Guo Liu Project Summary: The investigator proposes to develop and analyze efficient, accurate, and reliable numerical methods for unsteady viscous incompressible flows in the presence of boundaries with large Reynolds number, in hopes of simulating directly wall-generated turbulence. Efficient numerical computations of 3-D incompressible flow are currently far behind the practical needs. Indeed, even some very basic issues in formulating a numerical method are unsettled whenever boundaries are present, such as the correct numerical boundary conditions for the vorticity and efficient 3-D formulation. Some connections between different types of vorticity boundary formulations, such as local via global and the MAC scheme via Thom's formula, have already been found by this investigator and his collaborator Weinan E. With explicit treatment of the vorticity term and high-order (essentially) compact difference approach, they recently introduced a very efficient fourth order scheme in vorticity-stream function (vector) formulation, together with a complete convergence theory. The investigator proposes to continue developing efficient and accurate numerical methods for the three dimensional computation using both the vorticity-stream function and vorticity-velocity formulations. The investigator also plans to conduct a systematic study of statistical behavior and coherent structure of some 2-D and 3-D wall-bounded turbulence flows such as the driven cavity flow, backward-facing step flow, etc. and carry out a detailed numerical comparison with the homogeneous isotropic turbulence simulations. Extensive work has been done on direct simulation of isotropic turbulence in wall-free flows, much less work has involved wall-bounded turbulence. However, most turbulence is generated at the walls. Understanding turbulent flows is a grand challenge comp arable to other prominent scientific problems such as the large-scale structure of the universe and the nature of subatomic particles. In contrast to many of the other grand challenges, progress on the basic theory of turbulence translates nearly immediately into a wide range of engineering applications and technological advances that affect many aspects of everyday life. Direct numerical simulation for Navier-Stokes equation is an effective tool that complements experimental and theoretical investigation of turbulence. The investigator proposes to study two problems in the field: (1) Developing efficient, robust and reliable numerical methods for viscous incompressible flows in domains with solid boundaries, especially in the cases with large Reynolds number. (2) Using these methods to study statistical behavior and coherent structure of two and three dimensional wall-bounded turbulence via direct numerical simulations.

大型雷诺数数量的有效数值方法不稳定粘性不可压缩的流动刘伊·刘项目摘要：研究者建议在大型Reynolds编号的庞大的Reynolds数字中开发和分析不稳定的不稳定粘性不可压缩不可压缩流的高效，准确且可靠的数值方法。目前，3-D不可压缩流的有效数值计算远远落后于实际需求。实际上，即使存在边界时，即使是制定数值方法的一些非常基本的问题，例如涡度和有效的3-D公式的正确数值边界条件。 该研究者和他的合作者Weinan E之间已经发现了不同类型的涡度边界公式之间的某些连接，例如通过全球和MAC计划通过Thom的公式进行了连接，并明确处理了涡度期限和高阶（本质上）紧凑的差异方法，他们最近在涡流 - 曲线 - 基因源性（Vorticity-stream-stream-stream-stream-stream-stream-stream-stream-stream-stream-stream-stream-stream intery）（vector-stream-stream intery（Vector-stream-stream）中引入了A a A的组合。研究人员建议使用涡度 - 流函数和涡度 - 速度公式来继续为三维计算开发有效，准确的数值方法。 研究者还计划对一些二-D和3-D壁结合的湍流流的统计行为和相干结构进行系统研究，例如驱动的腔流，向后的阶梯流量等，并与同质的同型湍流模拟进行详细的数值比较。在无壁流中的各向同性湍流的直接模拟上进行了广泛的工作，涉及壁挂式湍流的工作要少得多。 但是，大多数湍流是在墙壁上产生的。 理解湍流是对其他突出的科学问题的巨大挑战，例如宇宙的大规模结构和亚原子颗粒的性质。与许多其他巨大的挑战相反，基本湍流理论的进步几乎立即转化为影响日常生活许多方面的广泛的工程应用和技术进步。 Navier-Stokes方程的直接数值模拟是一种有效的工具，可以补充湍流的实验和理论研究。 研究人员建议研究该领域的两个问题：（1）在具有固体边界的域中开发有效，健壮和可靠的数值方法，以探讨粘性不可压缩的流量，尤其是在雷诺数较大的情况下。 （2）使用这些方法通过直接数值模拟研究两维壁构成的湍流的统计行为和相干结构。