MIT OpenCourseWare

Browse materialsMIT 2.29 · Spring 2015

Numerical Fluid Mechanics

Subjects: Mathematics · Mechanical Engineering

Art: Frederick Collins, Collins steam engine drawing, 1918 · Public domain

Instructor: Prof. Pierre Lermusiaux
Term: Spring 2015
Level: Graduate
What's inside: 6 problem sets · 4 exams · 1 lecture note · 42 other files · 5 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 2.29 Numerical Fluid Mechanics, Spring 2015, Prof. Pierre Lermusiaux — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Formula sheets

License: CC BY-NC-SA 4.0 · MIT

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Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Numerical Linear Algebra · Fluid Mechanics · Fluid Mechanics · Fluid Mechanics

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

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MIT's page format for this item wasn't recognized clearly enough to place it safely. (9 items)
Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence.

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes and References

36 files

Assignments

12 files

Quizzes

MIT OpenCourseWare, Prof. Pierre Lermusiaux, 2.29 Numerical Fluid Mechanics, Spring 2015.

License: CC BY-NC-SA 4.0 · Edition: Spring 2015 · Open the original course on OCW ↗

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Numerical Fluid Mechanics

Formula sheets

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes and References

Assignments

Quizzes

Lecture 1: Introduction to Numerical Fluid Mechanics: Models to Simulations, Error Types. Approximation and Round-off Errors. Number Representations. Errors of Numerical Operations.

Lecture 2: Recursion. Truncation Errors, Taylor Series and Error Analysis. Error Propagation and Estimation. Condition Numbers. Roots of Non-linear Equations–introduction and Bracketing Methods.

Lecture 3: Roots of Non-linear Equations, Bracketing Methods: Bisection / False Position. Open Methods: Open-point Iteration / Newton-raphson / Secant Methods, Extension to Systems of Equations.

Lecture 4: Systems of Linear Equations: Motivations and Plans, Direct Methods, Gauss Elimination.

Lecture 5: Systems of Linear Equations. Gaussian Elimination (Special Cases, Multiple Right Hand Sides). LU Decomposition and Factorization, Pivoting. Error Analysis for Linear Systems. Operations Counts.

Lecture 6: Systems of Linear Equations. Special Matrices: LU Decompositions, Tri-diagonal Systems, General Banded Matrices, Symmetric, Positive-definite Matrices. Introduction to Iterative Methods.

Lecture 7: Systems of Linear Equations. Iterative Methods: Jacobi’s Method, Gauss-seidel Iteration, Convergence, Successive Over-relaxation Methods, Gradient Methods, Stop Criteria, Examples.

Lecture 8: End of Systems of Linear Equations: Gradient Methods, Pre-conditioning. Krylov Methods. Finite-differences (FD): Classification of PDEs and Examples, Error Types and Discretization Properties.

Lecture 9: FD Schemes: Finite Difference Based on Taylor Series for Higher Order Accuracy Differences. Examples. Taylor Tables or Method of Undetermined Coefficients.

Lecture 10: FD Schemes: Polynomial Approximations (Newton, Lagrange, Hermite and Pade Schemes), Iterative Improvements and Extrapolations, Boundary Conditions, Non-uniform Grids, Grid Refinement.

Lecture 11: Finite-differences: Fourier Error Analysis, Introduction to Stability: Heuristic, Energy and Von Neumann Methods, Hyperbolic PDEs, Characteristics.

Lecture 12: Stability, Hyperbolic Eqns. Revisited, CFL Condition and Von Neumann Stability, Elliptic Equations Revisited and FD Schemes.

Lecture 13: End of Elliptic / Hyperbolic Equations, Special Advection Schemes (Donor Cell, Flux-corrected Transport, WENO), Parabolic Equations Revisited and Numerical FD Schemes.

Lecture 14: Finite Volume Methods.

Lecture 15: Methods for Unsteady Problems. Time Marching Methods. Ordinary Differential Equations (ODEs). Initial Value Problems (IVPs). Euler’s Method. Runge-kutta Methods.

Lecture 16: Time Marching (cont.): Higher Order ODEs, Stiffness and Multistep Methods. Solutions of the Navier Stokes Equation, Incompressible and Compressible.

Lecture 17: Solutions of the Navier Stokes Equation: Incompressible and Compressible. Pressure-correction, Fractional Step.

Lecture 18: Solutions of the Navier Stokes Equation: Incompressible and Compressible. Vorticity, Artificial Compressibility and Other Methods.

Lecture 19: Grid Generation and complex Geometries.

Lecture 20: Finite Volume on Complex Geometries. Finite Element Methods: Introduction. Fluid Applications.

Lecture 21: Finite Element Methods (cont.): Continuous Galerkin and Discontinuous Galerkin Methods. Spectral Methods.

Lecture 22: Lecture / Recitation. Inviscid Flow Equations: Boundary Element Methods. Panel Methods.

Lecture 23: Turbulent Flows: Models and Numerical Simulations.

Lecture 24: Finite Volume on Complex Geometries: Turbulent Flows and Their Numerical Modeling.

Lecture 25: Turbulence