Computational fluid dynamics (CFD) has become an essential tool in the analysis and design of thermal and fluid flow systems in
wide range of industries. Few prominent areas of applications of CFD include meteorology, transport systems (aerospace, automobile, highspeed trains), energy systems, environment, electronics, bio-medical (design of life support and drug delivery systems), etc.
Correctly using CFD as a design analysis or diagnostic tool requires a thorough understanding of underlying physics, mathematical modeling, and numerical techniques. The user must be fully aware of the properties and limitations of the numerical techniques incorporated in CFD software. This course aims to provide precise insights into CFD.
Mathematical modeling: Governing equations of fluid flow and heat transfer; Introduction to discretization methods: Finite difference and finite volume methods for heat transfer problems; Time stepping methods for unsteady problems; Solution techniques for system of algebraic equations; Grid generation techniques; Solution techniques for Navier-Stokes equation; Finite element method for heat transfer and fluid flow problems; Turbulence modeling.
Competence
After the completion of the course the candidate will be able to…
- use the knowledge of mathematical modelling techniques and carry out computational fluid dynamic analysis of engineering problems within mechanical engineering.
- model and simulate the fluid flow related problems using available software tools.
- use the knowledge of verification and validation techniques, and evaluate the quality of the mathematical model, and demonstrate the reliability of results.
- communicate the results of modelled engineering problem through a scientific report and the presentations.
Contents
Introduction: Conservation equation; mass; momentum and energy equations; convective forms of the equations and general description.
Classification and Overview of Numerical Methods: Classification into various types of equation; parabolic elliptic and hyperbolic; boundary and initial conditions; over view of numerical methods.
Finite Difference Technique: Finite difference methods; different means for formulating finite difference equation; Taylor series expansion, integration over element, local function method; treatment of boundary conditions; boundary layer treatment; variable property; interface and free surface treatment; accuracy of f.d. method.
Finite Volume Technique: Finite volume methods; different types of finite volume grids; approximation of surface and volume integrals; interpolation methods; central, upwind and hybrid formulations and comparison for convection-diffusion problem.
Finite Element Methods: Finite element methods; Rayleigh-Ritz, Galerkin and Least square methods; interpolation functions; one and two dimensional elements; applications.
Methods of Solution:Solution of finite difference equations; iterative methods; matrix inversion methods;ADI method; operator splitting; fast Fourier transform.
Time integration Methods:Single and multilevel methods; predictorcorrector methods; stability analysis;Applications to transient conduction and advectiondiffusion problems.
Numerical Grid Generation: Numerical grid generation; basic ideas; transformation and mapping.
Navier-Stokes Equations:Explicit and implicit methods;SIMPLE type methods; fractional step methods.
Turbulence modeling: Reynolds averaged Navier-Stokes equations, RANS modeling, DNS and LES.
