Introduction to CFD

1 Basics of Discretization

1.1 Finite- Difference representation of Partial Differential Equations.

1.2 Truncation error, Round off and Discretization error.

1.3 Consistency, Stability and Convergence.

2 Two dimensional Laplace equation

2.1 Finite-Difference representation for Laplace’s equation.

2.2 Direct Methods

2.2.1 Cramer’s rule.

2.2.2 Gaussian elimination.

2.3 Iterative Methods

2.3.1 Jacobi iteration.

2.3.2 Guass Seidal iteration.

2.3.3 SOR.

3 One dimensional 1st order Linear wave equation

3.1 Finite-Difference representation of 1-D linear wave equation.

3.2 Euler explicit and implicit methods (FTFS, FTBS, FTCS, BTCS).

3.3 Von – Neumann stability analysis.

4 One dimensional Heat equation

4.1 Finite-Difference representation for 1-D Heat Equation.

4.2 Simple Explicit Method.

4.3 Simple Implicit Method.

Incompressible Fluid Flow

1 Basic Concepts in incompressible flows

1.1 Steady and unsteady flows.

1.2 Streamlines, pathlines, vorticity and circulation.

1.3 Reynold's Transport theorem.

2 Governing equations

2.1 Continuity Equation.

2.2 Momentum Equation.

3 Exact solution for the Navier – Stokes equations

3.1 Couette Flow.

3.2 Plane Poiseuille flow.

3.3 Couette – Poiseuille flow.

3.4 Stoke's I & II problem.

4 Potential flows

4.1 Source and sink flows.

4.2 Doublet flow.

4.3 Combination of flows.

5 Laminar Boundary Layer Theory.

5.1 Derivation of boundary layer.

5.2 Boundary Layer over a flat plate with zero pressure gradients.

5.2.1 Similarity Approach.

5.2.2 Integral Analysis.

5.3 Approximate solution (Karman – Pohlhausen method).

5.4 Displacement Thickness and Momentum Thickness.