Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Feb. 19
|
| Algebra and Number Theory
No Seminar
|
This is the second part of the talks on the topic. We examine how stationary solutions to Galerkin approximations of the Navier--Stokes equations behave in the limit as the Grashof number $G$ tends to $\infty$. An appropriate scaling is used to place the Grashof number as a new coefficient of the nonlinear term, while the body force is fixed. A new type of asymptotic expansion, as $G\to\infty$, for a family of solutions is introduced. Relations among the terms in the expansion are obtained by following a procedure that compares and totally orders positive sequences generated by the expansion. The same methodology applies to the case of perturbed body forces and similar results are obtained. We demonstrate with a class of forces and solutions that have convergent asymptotic expansions in $G$. All the results hold in both two and three dimensions, as well as for both no-slip and periodic boundary conditions. This is joint work with Ciprian Foias and Michael S. Jolly (Indiana University).
Abstract. We present the progress toward understanding the solution structures of transonic problems in multidimensional conservation laws. In applications such as the airflow near the wing tip for a high-speed aircraft or space shuttle, the flow makes an abrupt change in its direction, creating shock waves and turbulences depending on the contact angles and the speed of the aircraft. We have a well-known system, the compressible Euler system, to explain such applications and recent advancements in high-performing computing shed light on the shock configurations to understand such abrupt changes of the airflow near the wing. For some shock configurations, the governing system can be reduced in self-similar coordinates, making the problem more tractable to develop mathematical analysis. On the other hand, the system now changes it type, hyperbolic far from the locus of characteristics and mixed near the locus. I will present the mathematical advancements in understanding transonic problems for reduced systems.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 944 4492 2197
* Passcode: applied
 | Thursday
Feb. 22
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Jeff Lee
Mathematics and Statistics, Texas Tech University
|
Math Circle spring poster
abstract 2 PM CST (UT-6)