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Computational Fluid Dynamics using Finite Volume Method

Prof. Kameswararao Anupindi · IIT Madras

Start with lecture 1 At NPTEL

About

In this course, the discretization and solution of diffusion, convection-diffusion, and incompressible fluid flow equations are discussed. Finite volume method is used to discretize each of the equations. The discretization and solution methods are formulated on structured as well as unstructured meshes. This course involves hand-calculations on simple meshes as well as numerical programming of the algorithms discussed.

INTENDED AUDIENCE : Bachelors, masters and doctoral students, practicing scientists and engineers from industry.

PREREQUISITES : Courses on linear algebra, numerical methods, incompressible fluid mechanics, and heat transfer

Lectures

Week 1

  1. Review of governing equations: Conservation of mass YouTube
  2. Review of governing equations: Conservation of momentum YouTube
  3. Review of governing equations: Conservation of energy YouTube
  4. Review of governing equations: Navier-Stokes equations and energy equation YouTube

Week 2

  1. Review of governing equations: General scalar transport equation YouTube
  2. Review of governing equations: classification of PDEs YouTube
  3. Overview of Numerical Methods: Finite Difference Method YouTube

Week 3

  1. Overview of Numerical Methods: Finite Volume Method YouTube
  2. Overview of Numerical Methods: Solution of linear algebraic equations YouTube
  3. Finite Volume Method for Diffusion Equation : Discretization of 1D diffusion equation YouTube

Week 4

  1. Finite Volume Method for Diffusion Equation: Discretization of 2D diffusion equation YouTube
  2. Finite Volume Method for Diffusion Equation: Boundary conditions for 2D diffusion equation YouTube
  3. Finite Volume Method for Diffusion Equation: Discretization of 3D diffusion equation, mixed boundary conditions YouTube

Week 5

  1. Finite Volume Method for Diffusion Equation: Tri-Diagonal Matrix Algorithm YouTube
  2. Finite Volume Method for Diffusion Equation: Linearization of source term, line-by-line TDMA YouTube
  3. Finite Volume Method for Diffusion Equation: Problem solving using TDMA YouTube

Week 6

  1. Finite Volume Method for Diffusion Equation: Problem solving using line-by-line TDMA YouTube
  2. Finite Volume Method for Diffusion Equation: Steady diffusion in polar and axisymmetric coordinates YouTube
  3. Finite Volume Method for Diffusion: Discretization of unsteady diffusion equation YouTube

Week 7

  1. Finite Volume Method for Diffusion Equation: Unsteady diffusion time-stepping schemes YouTube
  2. Finite Volume Method for Diffusion Equation: Unsteady diffusion time-stepping schemes and Truncation errors of the FV schemes YouTube
  3. Finite Volume Method for Diffusion Equation: Truncation errors and stability analysis YouTube
  4. Finite Volume Method for Diffusion Equation: Stability analysis and steady diffusion in unstructured meshes. YouTube

Week 8

  1. Finite Volume Method for Diffusion Equation: Steady diffusion in unstructured meshes Part 1 YouTube
  2. Finite Volume Method for Diffusion Equation: Steady diffusion in unstructured meshes Part 2 YouTube
  3. Finite Volume Method for Diffusion Equation: Steady diffusion in unstructured meshes Part 3 YouTube

Week 9

  1. Finite Volume Method for Diffusion Equation: Steady diffusion in unstructured meshes Part 4 YouTube
  2. Finite Volume Method for Diffusion Equation: Steady diffusion in unstructured meshes Part 5 YouTube
  3. Finite Volume Method for Convection and Diffusion: Discretization of steady convection equation YouTube

Week 10

  1. Finite Volume Method for Convection and Diffusion: Discretization of steady convection equation YouTube
  2. Finite Volume Method for Convection and Diffusion: Discretization of steady and unsteady convection equation YouTube
  3. Finite Volume Method for Convection and Diffusion: Discretization of unsteady convection equation YouTube
  4. Finite Volume Method for Convection and Diffusion: Discretization of convection-diffusion equation on unstructured mesh YouTube

Week 11

  1. Finite Volume Method for Convection-diffusion and fluid flow calculations YouTube
  2. Finite Volume Method for Fluid Flow Calculations: The staggered grid approach YouTube
  3. Finite Volume Method for Fluid Flow Calculations: SIMPLE algorithm - part 1 YouTube
  4. Finite Volume Method for Fluid Flow Calculations: SIMPLE algorithm - part 2 YouTube
  5. Finite Volume Method for Fluid Flow Calculations: SIMPLE algorithm - part 3 YouTube

Week 12

  1. Finite Volume Method for Fluid Flow Calculations: SIMPLE-Revised and SIMPLE-Corrected algorithm YouTube
  2. Finite Volume Method for Fluid Flow Calculations: SIMPLE algorithm for Colocated mesh YouTube
  3. Finite Volume Method for Fluid Flow Calculations: SIMPLE algorithm for Colocated mesh YouTube
  4. Finite Volume Method for Fluid Flow Calculations: SIMPLE-Colocated algorithm for Unstructured mesh YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mechanical Engineering
Teacher
Prof. Kameswararao Anupindi
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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