JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

UNIT - I

Introduction to Numerical Methods - Finite Difference, Finite Element and Finite Volume Methods – Classification of Partial Differential Equations – Solution of Linear Algebraic Equations – Direct and Iterative Approaches Finite difference methods: Taylor’s series – FDE formulation for 1D and 2D steady state heat transfer problems – Cartesian, cylindrical and spherical co-ordinate systems – boundary conditions – Un steady state heat conduction – Errors associated with FDE - Explicit Method – Stability criteria – Implicit Method – Crank Nickolson method – 2-D FDE formulation – ADI – ADE

UNIT - II

Finite Volume Method: Formation of Basic rules for control volume approach using 1D steady heat conduction equation – Interface Thermal Conductivity - Extension of General Nodal Equation to 2D and 3D Steady heat conduction and Unsteady heat conduction

UNIT - III

FVM to Convection and Diffusion: Concept of Elliptic, Parabolic and Hyperbolic Equations applied to fluid flow – Governing Equations of Flow and Heat transfer – Steady 1D Convection Diffusion – Discretization Schemes and their assessment – Treatment of Boundary Conditions

UNIT - IV

Calculation of Flow Field: Vorticity& Stream Function Method - Staggered Grid as Remedy for representation of Flow Field - Pressure and Velocity Corrections – Pressure Velocity Coupling - SIMPLE & SIMPLER (revised algorithm) Algorithm.

UNIT - V

Turbulent Flows: Direct Numerical Simulation, Large Eddy Simulation and RANS Models Compressible Flows: Introduction - Pressure, Velocity and Density Coupling.

REFERENCES:

• 1. Numerical heat transfer and fluid flow – S.V. Patankar (Hemisphere Pub. House)
• 2. An Introduction to Computational Fluid Dynamics – FVM Method – H.K. Versteeg, W. Malalasekhara (PHI)
• 3. Computational Fluid Flow and Heat Transfer – Muralidharan & Sundarajan (Narosa Pub)
• 4. Computational Fluid Dynamics – Hoffman and Chiang, Engg Education System
• 5. Computational Fluid Dynamics – Anderson (TMH)
• 6. Computational Methods for Fluid Dynamics – Ferziger, Peric (Springer)
• 7. Computational Fluid Dynamics, T.J. Chung, Cambridge University
• 8. Computaional Fluid Dynamics – A Practical Approach – Tu, Yeoh, Liu (Elsevier)
• 9. Text Book of Fluid Dynamics, Frank Chorlton, CBS Publishers