Introduction:
History and Philosophy of computational fluid dynamics, CFD as a design and research tool, Applications of CFD in engineering, Programming fundamentals, MATLAB programming, Numerical Methods
Governing Equations:
Models of the flow, The substantial derivative, Physical meaning of the divergence of velocity, The continuity equation, The momentum equation, The energy equation, NavierStokes equations for viscous flow, Euler equations for inviscid flow, Physical boundary conditions, Forms of the governing equations suited for CFD
Partial differential equations:
Classification of quasi-linear partial differential equations, Methods of determining the classification, General behaviour of Hyperbolic, Parabolic and Elliptic equations.
Basic aspects of discretization:
Introduction to finite differences, Finite difference equations using Taylor series expansion and polynomials, Explicit and implicit approaches, Uniform and unequally spaced grid points
Grids with appropriate transformation:
General transformation of the equations, Metrics and Jacobians, The transformed governing equations of the CFD, Boundary fitted coordinate systems, Algebraic and elliptic grid generation techniques, Adaptive grids.
Parabolic partial differential equations:
Finite difference formulations, Explicit methods – FTCS, Richardson and DuFortFrankel methods, Implicit methods – Crank-Nicolson and Beta formulation methods, Approximate factorization, Fractional step methods, Consistency analysis, Linearization
Elliptic equations:
Finite difference formulation, solution algorithms: Jacobi-iteration method, Gauss-Siedel iteration method, point- and line-successive over-relaxation methods, alternative direction implicit methods.
Hyperbolic equations:
Explicit and implicit finite difference formulations, splitting methods, multi-step methods, applications to linear and nonlinear problems, linear damping, flux corrected transport, monotone and total variation diminishing schemes
Stability analysis:
Discrete Perturbation Stability analysis, von Neumann Stability analysis, Error analysis, Modified equations, Artificial dissipation and dispersion.
Grid generation:
Algebraic Grid Generation, Elliptic Grid Generation, Hyperbolic Grid Generation, Parabolic Grid Generation
Course outcomes:
At the end of the course the student will be able to:
CO1: Understand the stepwise procedure to completely solve a fluid dynamics problem using computational methods
CO2:Derive the governing equations and understand the behaviour of the equations
CO3: Identify the boundary conditions and apply for the given problem.
CO4:Analyze the consistency, stability and convergence of various discretization schemes for parabolic, elliptic and hyperbolic partial differential equations.
CO5:Analyze methods of grid generation techniques and apply the finite difference and finite volume methods to solve the problems.
Question paper pattern:
The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.
Textbook/ Textbooks
1) Anderson, J.D(Jr) Computational Fluid Dynamics McGraw-Hill Book Company 2nd Edition, 2017
) Hoffman, K.A., and Chiang, S.T Computational Fluid Dynamics, Vol. I, II and III, Engineering Education System, Kansas, USA 2nd Edition, 2000
Reference
1) Chung, T.J Computational Fluid Dynamics, Cambridge University Press 2nd Edition, 2014
2) Versteeg, H.K. and Malalasekara, W., An Introduction to Computational Fluid Dynamics Pearson Education 2nd Edition, 2010
3) Anderson, D.A., Tannehill, J.C., and Pletcher, R.H., CRC Press 3rd Edition, 2013.