Department
Home Page
About Us:
• Contact Info.
• Faculty
• Staff
• Students
Academic Program:
• Admission
• Undergraduate
• Graduate
• Certificates
Courses:
• Course Description
• Class Web Pages
• Class Syllabi
• Skills Tests
Research:
• Research Groups
• Colloquium
• Seminars
• News
Links:
| • Alumni Questionnaire |
| • Math Lab |
| • CAPA & Skills Tests |
| •Math Placement Test |
| • UCF Math Club |
| • Academic System Lab |
| • Careers |
| • American Mathematical Society |
| • Mathematical Association of America |
02/13/01 Colloquium
PROFESSOR JIE SHEN
Department of Mathematics
Pennsylvania State University
Department of Mathematics
Pennsylvania State University
Some New Developments on Projection Methods for Incompressible Flows
Abstract: The projection method, initially proposed by Chorin and Temam in the later 60's, has played and is still playing a major role in computational fluid dynamics. However, the intrinsic mechanisms of various versions of the projection method are still not fully understood. In particular, there is still no rigorous theoretical justification for the class of very successful schemes proposed by Orszag, Isreali & Deville (1986) and Karniadakis, Isreali & Orszag (1991). I will start with a review of the projection-type methods for incompressible flows. Then, I will introduce the rotational form of the pressure-correction projection method and a new class of velocity-correction projection methods. I will show that the rotational forms of the pressure-correction and velocity-correction schemes provide consistent Neumann boundary condition for the pressure approximation, and consequently, lead to improved error estimates. Furthermore, I will show that the schemes proposed by Orszag, Isreali & Deville (1986) and Karniadakis, Isreali & Orszag (1991) can be reinterpreted as rotational forms of our velocity-correction projection methods. Numerical results, obtained using a spectral-projection method, on three-dimensional rotating flows in an enclosed cylinder will be presented.