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July 30, 2022


Unlimited Duration


This course includes:

Unlimited Duration

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Unlimited Duration


This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations.

Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).

Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for their contributions to the course over the years.

Course Curriculum

  • Introduction to Numerical Fluid Mechanics: Models to Simulations Unlimited
  • Truncation Errors, Taylor Series and Error Analysis. Unlimited
  • Roots of Non-linear Equations Unlimited
  • Systems of Linear Equations: Motivations and Plans, Direct Methods, Gauss Elimination. Unlimited
  • Systems of Linear Equations. Gaussian Elimination (Special Cases, Multiple Right Hand Sides) Unlimited
  • Systems of Linear Equations. Special Matrices: LU Decompositions, Unlimited
  • Lecture 7 Unlimited
  • Lecture 8 Unlimited
  • Lecture 9 Unlimited
  • Lecture 10 Unlimited
  • Lecture 11 Unlimited
  • Lecture 12 Unlimited
  • Lecture 13 Unlimited
  • Lecture 14 Unlimited
  • Lecture 15 Unlimited
  • Lecture 16 Unlimited
  • Lecture 17 Unlimited
  • Lecture 18 Unlimited
  • Lecture 19 Unlimited
  • Lecture 20 Unlimited
  • Lecture 21 Unlimited
  • Lecture 22 Unlimited
  • Lecture 23 Unlimited
  • Lecture 24 Unlimited
  • Lecture 25 Unlimited

About the instructor

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Massachusetts Institute of Technology