Computational Heat and Fluid Flow (ME 605)

ME 605 is an elective course for B.Tech, M.Tech, and PhD students of the school of mechanical sciences, Indian Institute of Technology Goa. This page containts details of the course that is being taught during Spring 2021.

Instructors: Dr. Rudra Narayan Roy and Dr. Sudhakar Yogaraj

Teaching Assistant: Dheeraj R

Course contents

• Preliminaries: Continuum approximation, governing equations for fluid flow and heat transfer, introduction to computational fluid dynamics

• Finite difference method: Taylor series, backward, forward and central differences, truncation error, discretization of 1D diffusion equation, TDMA and Gauss-Seidel method

• Finite volume method for diffusion problems: Control volume approach, basic rules, Discretization and solution of 1D diffusion equations, boundary conditions, unsteady 1D diffusion equation, explicit, Crank-Nicolson and implicit schemes, 2D and 3D situations

• Finite volume method for convection-diffusion equations: Failure of central schemes, properties of discretization schemes, upwind, QUICK, hybrid and power law schemes, 2D and 3D discretized equations

• Finite volume method for 1D nonlinear equations: review of iterative methods of N ewton and Picard, Solution of Burgers equation

• Finite volume method for Navier-Stokes equations: Navier-Stokes equations, related difficulties, staggered grid, SIMPLE, SIMPLER, SIMPLEC and PISO, fractional step Method

Example codes

• Finite difference approximation to first and second derivatives [python] [matlab][C/C++]

• Explicit time integration for 1D diffusion equation [python] [matlab] [C/C++]

• Finite volume solution of Burgers equation with Newton's method for linearization [python] [matlab]

Reference books

• H Versteeg, W Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Printice Hall 2007.

• SV Patankar, Numerical Heat Transfer and Fluid Flow, CRC Press 1980.

• JD Anderson, Computational Fluid Dynamics: The Basics with Applications, McGraw Hill education 2017.

• JH Ferziger, M Peric, Computational Methods for Fluid Dynamics, Springer 2002.