Computational Fluid Dynamics

Unit 1

Introduction and Basic Concepts:

Introduction of CFD, Types of fluids and basic equations of flow, Mass Conservation, Newton’s second law of motion, Fluid flow governing equations, Navier- stokes equation, Boundary layer equations, Expanded form of Navier-stokes equations, Conservation of energy principle, Special form of energy equation, Classification of second order partial differential equations, Initial and Boundary conditions, Governing equations in generalized coordinates, Review of essentials of fluid dynamics.

Unit 2

Differential Equations and Discretisation Elementary Finite Difference Equations, Basic aspects of finite difference equations, errors and stability analysis, discretization, Taylor’s series expansion, difference equation: explicit and implicit approach, Application to heat conduction and convection, problems on one dimension steady state and unsteady state conduction.

Unit 3

Grid Transformation Introduction, general transformation equations, matrices and Jacobean, transformed version of governing equation particularly suited for CFD, compressed grids, elliptic grid generation, adaptive grids

Unit 4

Introduction to finite element philosophy Basics of finite element method, stiffness matrix, Isoperimetric elements, Formulation of finite elements for flow and heat transfer problems.

Unit 5

Introduction to finite volume philosophy: Integral approach, discretization and higher order schemes, Application to complex geometry.