Singularly Perturbed Convection Diffusion Problems

Kopriva, DavidFrom: R. Bruce Kellogg [kellogg@ipst.umd.edu]发送：Thursday， May 31, 2001 6:04 AMTo: dkopriva@nsf.govCc: kellogg@ipst.umd.eduSubject：提案号：0101563 - abstract提案号：0101563 - abstract将研究与奇异摄动边值问题相关的一些数学和数值分析问题。数学问题包括得到考虑边界层、内层和角点奇点的解的导数的明确界限。数值问题包括这些奇异摄动问题的稳定离散化的发展和奇异摄动问题的最佳逼近性质的研究。拟议的工作研究物理系统，其中某些数量在某些区域经历快速变化。这样的系统包括流体流动，其中快速变化发生在边界层、激波和内层。这些系统出现在流体机械的设计、地下油水输送的研究、汽车和飞机上空气流的建模以及其他领域。这项研究的结果将用于开发这些系统的更精确的计算机模拟，从而改进用于此类现实问题的设备设计。此外，该提案规定M. Stynes教授定期访问美国；Stynes教授计划与在相关领域工作的数学研究生进行互动。

Kopriva, DavidFrom: R. Bruce Kellogg [kellogg@ipst.umd.edu]Sent: Thursday, May 31, 2001 6:04 AMTo: dkopriva@nsf.govCc: kellogg@ipst.umd.eduSubject: Proposal No: 0101563 - AbstractProposal No: 0101563 - AbstractSome problems of mathematical and numerical analysis related tosingularly perturbed boundary value problems will be studied. Themathematical problems include obtaining sharp bounds for derivatives ofthe solution that take into account boundary layers, interior layers, andcorner singularities. The numerical problems include the development ofstabilized discretizations for these singularly perturbed problems andthe study of the best approximation properties of singular perturbationproblems.The proposed work studies physical systems in which some quantitiesundergo rapid changes in certain regions. Such systems include fluid flow,where the rapid changes occur at boundary layers, shocks, and interiorlayers. These systems arise in the design of fluid machinery, the studyof underground oil and water transport, the modeling of airflow overcars and airplanes, and other areas. The results of this research willbe of use in the development of more accurate computer simulations ofthese systems, with consequent improvements in the design of equipmentused in such real-world problems. In addition, the proposal providesfor regular visits of Professor M. Stynes to the U.S.; it is plannedthat Prof. Stynes will interact with graduate students in mathematics whoare working in related areas.