Computational Fluid Dynamics

Motivation for CFD & Introduction to the CFD approach

Illustration of the CFD approach through a worked out example

Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Part 1

Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Part 2

Forces acting on a Control Volume: Stress tensor

Kinematics of deformation in fluid flow: Stress vs Strain Rate Relation

Equations governing flow of incompressible flow

Spatial discretization of a simple flow domain

Finite Difference Approximation of pth Order of Accuracy for qth Order Derivative

One-sided high order accurate approximations, Explicit & Implicit Formulations

Numerical solution of the unsteady advection equation using different finite

Need for analysis of a discretization scheme

Statement of the stability problem

Consistency and stability analysis of the unsteady diffusion equation

Stability analysis of the generic scalar equation

Template for the generic scalar transport equation and its extension to the solution

Illustration of application of the template using the MacCormack scheme

Stability limits of MacCormack scheme

Artificial compressibility method and the streamfunction-vorticity method

Pressur e equation method for the solution of NS equations

Pressure-correction approach to the solution of NS equations on a staggered grid

Need for effici ent solution of linear algebraic equations

Direct methods for linear algebraic equations & Gaussian elimination method

Gauss-Jordan method, LU decomposition method, TDMA & Thomas algorithm

Basic iterative methods for linear algebraic equations

Convergence analysis of basic iterative schemes, Diagonal dominance condition

Application to the Laplace equation

Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting

Advanced iterative methods, Strongly Implicit Procedure, Conjugate gradient method

Illustration of the Multigrid method for the Laplace equation

Numerical solution of NS equations for simple domains

Derivation of the energy conservation equation

Derivation of the species conservation equation & Dealing with chemical reactions

Turbulence, Characteristics of turbulent flow, Dealing with fluctuations

Derivation of the Reynolds – averaged Navier – Stokes equations

Reynolds stresses in Turbulent flow, Time & Length scales of Turbulence

One-equation model for turbulent flow

Two -equation model for turbulent flow & Numerical calculation of turbulent

Calculation of near-wall region in turbulent flow & wall function approach

Need for special methods for dealing with irregular fl ow geometry

Transformation of the governing equations & Illustration for the Laplace equation

Finite volume method for complicated flow domain

Finite volume method for the general case

Generation of a structured grid for irregular flow domain & Algebraic methods

Unstructured grid generation & Domain nodalization

Delaunay triangulation method for unstructured grid generation

Co-located grid approach for irregular geometries & Pressure correction equations