Offered courses in the past semesters:
VM235 Fundamentals of thermodynamics (undergrad)
VM432 Combustion (grad + undergrad)
VM505 Finite element analysis and computational mechanics (grad + undergrad)
Regularly offered courses:
VM523 Computational fluid dynamics (grad)
Textbook: Essential Computational Fluid Dynamics, Oleg Zikanov, 2010, John Wiley & Sons, Inc.
Course description: Governing Equations and Discretization / Integration Fundamentals
Compressible Navier-Stokes / Euler equations;
Incompressible Navier-Stokes / Euler equations
Cartesian Grids, structured grids, and unstructured grids;
Finite difference method, brief introduction of finite volume and finite element methods
Numerical solution of some simple equations: Upwind methods; Upwinding for a scalar equation; Boundary conditions; Extension to higher-order accuracy: Explicit time-stepping methods
Project:
- numericalsolution of the incompressible Navier-Stokes equations
- numericalsolution of the compressible Navier-Stokes equations
Topic discussion (turbulence modeling, LES etc.)
VM524 Turbulence (grad)
Textbook:
Turbulent Flows, S. Pope, Cambridge (2000);
A First Course in Turbulence, H. Tennekes and J.L. Lumley, MIT 1972
Course Description: Introduction: turbulence in nature and science; the nature of turbulence
Methods of analysis: dimensional analysis, local invariance, mathematical description, Karman-Harwarth equation
Scales in turbulence: energy cascade, Kolmogorov hypothesis
Free shear turbulence: jet flow and self-similarity
Wall shear turbulence: mean profiles, Reynolds stress, length scales
Passive scalar transport in turbulence:
Introduction of turbulence modeling and simulation: direct numerical simulation, turbulence modeling
VM320 Fluid mechanics (undergrad)
Textbook: Fluid mechanics, 4th edition, by Pijush K. Kundu, Ira M. Cohen
Course description:
Chapter 1: Introduction: Field phenomena: compared with systems consisting of isolated particles; concepts of solids and fluids; continuum hypothesis; transport phenomena; surface tension; basis review of thermodynamics; static equilibrium
Chapter 2:Bases of vector analysis: Space and coordinate; rotation of axes; second-order tensor and tensor contraction; Kronecker Delta and alternating symbol; dot and cross product; divergence and gradient operators; symmetric and antisymmetric tensors; Eigenvalues and eigenvectors of a symmetric tensor or a symmetric matrix; Multi-variables functions; force on a surface; Gauss and Stokes’ theorems;
Chapter 3: Kinematics: Eulerian and Lagrangian descriptions; Streamline, path line streak line; Strain rate; Vorticity and circulation; Relative motion near a point; Strain rate and angular velocity; Solid body motion and irrotation vortex; 1D, 2D and 3D flows
Chapter 4: Conservation laws: 1D Leibnitz theorem; The derivatives of volume integrals; Conservation of mass; Momentum conservation; Constitutive equation for Newtonian fluids; Navier-Stokes equation; Application of the Reynolds transport theorem; Rotating coordinate system; mechanical energy equation; Mechanical energy equation; Bernoulli equation; Boussinesq approximation; Boundary conditions
Chapter 6: Laminar flows: Steady flow between parallel plates; Steady flow in a pipe; Rotating flows; Impulsive started plate; Flow due to an oscillating plate; Reynolds number; creeping flow around a spherical surface.
Chapter 7: Dynamics similarity: For systems with deterministic governing equations; systems without explicit governing equations; Common nondimensional parameters.
Chapter 8: Boundary layers and related topics: Basic idea; Different measures of boundary layer thickness; Boundary layer on a flat plate; Structure of boundary layers; Von Karman momentum integral; Boundary layer with pressure gradient; Flow past a cylinder, sphere and the application to physical objects; 2D jets; Secondary flows; Decay of a laminar shear flow;
(Chapter 9(selective): Turbulence: Some basic concepts; Averaged equations)
Chapter 10: Compressible flows: Compressibility; Speed of sound; Basic relations for 1D flow; Area-velocity relations; Normal shock wave