Singularly Perturbed Convection-Diffusion Problems

奇扰动对流扩散问题

• 批准号: 0303684
• 负责人: Bruce Kellogg
• 金额: $ 0.84万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0303684&HistoricalAwards=false
• 关键词: Singularly; Perturbed; Convection; Diffusion; Problems

NSF Award Abstract - DMS-0303684Mathematical Sciences: Singularly Perturbed Convection-diffusion ProblemsAbstract0303684 Kellogg This project will establish establish sharp pointwise bounds on the derivatives of the solution of a singularly perturbed convection-diffusion problem in a polygonal domain, with an emphasis on the interaction between boundary layers and corner singularities and under the assumption of arbitrary smoothness of the data. The work will also develop applications of these bounds in numerical algorithms.This project investigates some differential equations of the type used in modeling fluid flow and transport. Emphasis is placed on properties of solutions with rapid transitions arising from boundary layers and corner singularities. These properties relate to the underlying solution structure, the competing effects of diffusion, convection and boundary irregularities (corners) contributing to this structure, and the resulting numerical approximability of the solutions. The award supports travel for collaborative research between Martin Stynes, University College, Cork, Ireland, and Bruce Kellogg, University of South Carolina.

NSF奖摘要- DMS-0303684数学科学：凯洛格本项目将建立多边形区域中的奇异摄动对流扩散问题的解的导数的尖逐点界，强调边界层和角点奇异性之间的相互作用，并假设数据是任意光滑的。 本研究也将发展这些界限在数值演算法上的应用。本计画探讨一些用于流体流动与输运的微分方程式。 重点放在快速过渡所产生的边界层和角奇异的解决方案的属性。 这些属性涉及到的基本解决方案的结构，扩散，对流和边界的不规则性（角落），有助于这种结构的竞争效应，以及由此产生的数值逼近的解决方案。 该奖项支持马丁Stynes，大学学院，科克，爱尔兰和布鲁斯凯洛格，南卡罗来纳州大学之间的合作研究旅行。