Mathematical Modeling of Fluid Flows
This course provides a mathematical introduction to the behavior of fluid flows, bridging the gap between fundamental principles and the modeling of complex phenomena. The first part of the course is dedicated to the derivation and physical interpretation of the Navier-Stokes equations, along with classical exact solutions and simplifications (potential flow, boundary layer theory). Building on this foundation, the second half explores the mathematical formulation of flow instabilities and the statistical treatment of turbulence. Students will examine various modeling paradigms, including eddy-viscosity models and Reynolds-Averaged Navier-Stokes (RANS) approaches, with an emphasis on the underlying assumptions, derivations, and applicability of each model.
Lecturer
Date
24th March ~ 16th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-4-312 | ZOOM 01 | 928 682 9093 | BIMSA |
Reference
1. Pope, S. B. - Turbulent Flows (Cambridge University Press, 2000)，经典湍流理论教材，涵盖统计理论与建模方法；
2. Wilcox, D. C. - Turbulence Modeling for CFD (DCW Industries, 2006)，详细介绍湍流模型，适合CFD相关研究；
3. Davidson, P. A. - Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, 2015)，强调物理概念，适合入门和中级学习；
4. Lesieur, M. - Turbulence in Fluids (Springer, 2008)，侧重于理论分析，适合研究导向的学习。
2. Wilcox, D. C. - Turbulence Modeling for CFD (DCW Industries, 2006)，详细介绍湍流模型，适合CFD相关研究；
3. Davidson, P. A. - Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, 2015)，强调物理概念，适合入门和中级学习；
4. Lesieur, M. - Turbulence in Fluids (Springer, 2008)，侧重于理论分析，适合研究导向的学习。
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Zhiting Ma obtained the B.S. degree from Lanzhou University in 2015 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University, China in 2021. Then, she worked as a postdoc at School of Mathematical Sciences, Peking University. Currently, she is an Assistant Professor in Beijing Institute of Mathematical Sciences and Applications (BIMSA). Her current research interests include kinetic theory, machine learning and hyperbolic relaxation systems.