## ME2032 COMPUTATIONAL FLUID DYNAMICS Lecture Notes for MECH - Seventh (7th) semester

ME2032 Lecture Notes

syllabus :

PREREQUISITE:
Fundamental Knowledge of partial differential equations, Heat Transfer and Fluid
Mechanics
UNIT I GOVERNING EQUATIONS AND BOUNDARY CONDITIONS
Basics of computational fluid dynamics – Governing equations of fluid dynamics –
Continuity, Momemtum and Energy equations – Chemical species transport – Physical
boundary conditions – Time-averaged equations for Turbulent Flow – Turbulent–Kinetic
Energy Equations – Mathematical behaviour of PDEs on CFD - Elliptic, Parabolic and
Hyperbolic equations.

UNIT II FINITE DIFFERENCE METHOD
Derivation of finite difference equations – Simple Methods – General Methods for first
and second order accuracy – solution methods for finite difference equations – Elliptic
equations – Iterative solution Methods – Parabolic equations – Explicit and Implicit
schemes – Example problems on elliptic and parabolic equations.

UNIT III FINITE VOLUME METHOD (FVM) FOR DIFFUSION
Finite volume formulation for steady state One, Two and Three -dimensional diffusion
problems. One dimensional unsteady heat conduction through Explicit, Crank –
Nicolson and fully implicit schemes.

UNIT IV FINITE VOLUME METHOD FOR CONVECTION DIFFUSION
Steady one-dimensional convection and diffusion – Central, upwind differencing
schemes-properties of discretization schemes – Conservativeness, Boundedness,
Trasnportiveness, Hybrid, Power-law, QUICK Schemes.

UNIT V CALCULATION FLOW FIELD BY FVM
Representation of the pressure gradient term and continuity equation – Staggered grid –
Momentum equations – Pressure and Velocity corrections – Pressure Correction
equation, SIMPLE algorithm and its variants. Turbulence models, mixing length model,
Two equation (k-Ð„) models – High and low Reynolds number models