Unit 1

Introduction & conservation laws of fluid motion: Models of the fluid flow, Substantial derivative, Divergence of the velocity, Laws of Conservation – Continuity Equation, momentum Equation, Energy Equation, Dimensionless forms of Equations, Simplified Mathematical Model, Mathematical Classification of flows, Physical Boundary conditions.

Basics of numerics: Components of the Numerical solution Methods – Mathematical model, Discretization method, Co-ordinates and Basic Vector systems, Numerical Grid, Finite approximations, Solution Method, Convergence criteria. Properties of Numerical Solution Methods – Consistency, Stability, Convergence, Conservativeness, Boundedness, Realizability. Discretization Approaches – FEM, FDM, FVM.

Unit 2

Finite difference method: Approximation of the first Derivative – Taylor series expansion, Polynomial Fitting, Compact Schemes, Non-Uniform Grids. Approximation of the second derivative, Approximation of the mixed derivative, Explicit and Implicit approaches, Errors and Analysis of stability.

Spectral analysis and grid generation: Spectral Analysis of numerical Schemes, Higher order methods, High accuracy compact schemes. General transformation of the equations, Matrics and Jacobians, Stretched grids, Boundary fitted Coordinate systems, Elliptic grid generation, unstructured grids.

Unit 3

• Ferziger J. H. and Peric M. – ‘Computational Methods for Fluid Mechanics’ – Springer – 2013 – 3rd Edition.
• Anderson J. D. – ‘Computational Fluid Dynamics: The Basics with applications’ – McGraw Hill – 2007

• Sengupta T. K. – ‘Fundamentals of Computational Fluid Dynamics’ – Universities Press – 2004
• Patankar S. V. – ‘Numerical Heat transfer and Fluid Flow’ – Taylor & Francis Publications – 1980