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


  1. numericalsolution of the incompressible Navier-Stokes equations
  2. numericalsolution of the compressible Navier-Stokes equations

Topic discussion (turbulence modeling, LES etc.)

VM524 Turbulence (grad)


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