An Adaptive Hybrid (Cartesian-Prism) Grid and Flow Solver for Navier-Stokes Equations

纳维-斯托克斯方程的自适应混合（笛卡尔棱镜）网格和流求解器

• 批准号: 9460372
• 负责人: Z.J. Wang
• 金额: $ 7.5万
• 依托单位: CFD RESEARCH CORPORATION
• 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: 1995-01-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9460372&HistoricalAwards=false
• 关键词: Adaptive; Hybrid; Cartesian; Prism; Grid

This Small Business Innovation Research Phase I project proposes to use overlapped Cartesian grid and Body-Fitted (BF) prism grids for solving viscous flow problems. Given a geometry definition in the form of triangularized surfaces, a BF prism mesh will be generated using the advancing layers technology with grid clustering near body surfaces. This prism mesh is then overlapped with a coarse uniform Cartesian background grid. Initially the Cartesian grid will be refined to have similar resolution near the prism grid. A high-order flow solver based on linear reconstruction and Roe's flux-difference splitting will be developed. Grid adaptation according to the physical nature of the flow field will be carried out to place control volumes where required the most, achieving maximum accuracy with minimum resources. An explicit multi-grid procedure will be employed to speed up the simulation process. The interface between the Cartesian and prism grid will be treated by conserving mass, momentum and energy flux on the outer boundary of the prism grid. The overall algorithm integrates grid generation and flow solver into one complete system to obtain maximum solution accuracy, efficiency and user friendliness. In Phase I, the above methodology will be implemented and demonstrated for 2-D viscous flow problems. Extension to 3-D and moving body problems and implementation in a commercial code will be made in Phase II.

这个小型企业创新研究第一阶段项目建议使用重叠笛卡尔网格和贴体（BF）棱柱网格来解决粘性流动问题。给定三角化表面形式的几何定义，将使用在身体表面附近网格聚类的推进层技术生成BF棱柱网格。然后将该棱柱网格与粗略的均匀笛卡尔背景网格重叠。最初，笛卡尔网格将被细化，以具有与棱镜网格相似的分辨率。将开发基于线性重构和Roe通量-差分分裂的高阶流动求解器。根据流场的物理性质进行网格自适应，将控制量放置在最需要的地方，以最少的资源实现最大的精度。一个显式的多重网格程序将加快模拟过程。笛卡尔网格和棱柱网格之间的界面将通过在棱柱网格的外边界上保持质量、动量和能量通量来处理。整个算法将网格生成和流场求解器集成到一个完整的系统中，以获得最大的解的精度，效率和用户友好性。在第一阶段，上述方法将被实施，并证明为二维粘性流问题。扩展到三维和移动体的问题和商业代码的实施将在第二阶段。