Courses Detail Information
ME6201J – Advanced Fluid Mechanics
Instructors:
Credits: 3 credits
Pre-requisites: Mathematic courses: calculus, vector analysis Mechanics courses: theoretical mechanics, thermodynamics, fluid mechanics
Description:
Based on the fluid mechanics course at the undergraduate level, VM520 aims to solidify the important concepts and the analytical skills, including the solutions of the N-S equations (including exact solutions, exact solutions of the approximate equations, approximate solutions of the differential equations, integral solutions and solutions from dimensional arguments), stability analyses, stochastic analyses etc. Students after this course are expected to gain fundamental insights of the fluids mechanics at the research level, even with the capability to initialize some topics of value for fundamental research. The objectives can be summarized as
1. to understand the physical concepts of flowing phenomenon;
2. to develop the capability of flow physics analysis;
3 to be able to simplify the complex problems in a reasonable way and extract the essential physics with the help of advanced analyses.
Course Topics:
Basic concepts review 1: continuum, transport phenomenon, surface tension
Basic concepts review 2: solids and fluids, shear stress, fluid statistics
Vector analysis 1: coordinate and system, first order tensor
Vector analysis 2: stress tensor, second—order tensor
Conservation laws1: Reynolds transports theorem, mass conservation
Conservation laws2: momentum conservation and energy conservation
Conservation laws3: constitutive relations and the boundary conditions of the equations
Analytical solutions 1: exact solutions
Analytical solutions 2: exact solution of the approximate equations
Analytical solutions 3:applications of the Reynolds transport theorem
Analytical solutions 4:applicaions of the RTT+ dimensional argument
Special topic 1: Boundary layer 1: basic concepts and the governing equations
Special topic 1: Boundary layer 2: Balsius solution and the results analysis
Special topic 1: Boundary layer 3: Symmetry analysis of the Blasius solution
Special topic 2: Stability analyses: introduction of the basic physics and the approximation of the equation
Special topic 2: Thermal instability
Special topic 2: Double-diffusive instability
Special topic 2: Centrifugal instability
Special topic 2: Instability of parallel flows
Special topic 2: Effects of viscousity
Special topic 3: Stochastic analyses: introduction
Special topic 3: Markov process
Special topic 3: Langevin equation
Special topic 3: Kramers-Moyal coefficient
Special topic 3: Fokker-Planck equation