Mathematical properties of Fluid Dynamics Equations ‐ Elliptic, Parabolic and Hyperbolic equations‐ Initial and Boundary conditions ‐ Well posed‐ ill Posed problems; Discretization of partial differential equations; Grid generation – Introduction, types of grids – structured, unstructured, single and multi‐block grids, hybrid and adaptive grids; Meshless methods; Explicit finite difference methods of subsonic, supersonic and viscous flows‐ Implicit and explicit schemes; Source panel method ‐ Vortex panel method Lab experiments: ● CFD simulation of the flow around the circular cylinder using open source software ● Large Eddy simulation analysis of various Airfoil using open source software
Boundary layer equations and methods of solution; Implicit time dependent methods for inviscid and viscous compressible flows ‐ Concept of numerical dissipation ‐‐Stability properties of explicit and implicit methods ‐ Conservative upwind discretization for hyperbolic systems ‐ Further advantages of upwind differencing. Lab experiments: ● Numerical simulation of flow through C-D nozzle ● Numerical simulation of flow through Turbine blade passage
Finite Element Techniques in Computational Fluid Dynamics; Introduction ‐ Strong and weak formulations of a boundary value problem ‐ Strong formulation ‐ Weighted residual formulation ‐Galerkin formulation; Weak formulation ‐ Variational formulation ‐ Piecewise defined shape functions; Implementation of the FEM ‐ The solution procedure. Lab experiments: ● Evaluation of openFOAM performance for RANS simulations of flow around a NACA 4412 airfoil ● Numerical Structural Analysis of a Tapered wing structure
Finite Volume Techniques ‐ Cell centered formulation ‐ Lax – Wendroff time stepping, Runge‐Kutta time Stepping ‐ Multi‐stage time stepping; Accuracy Cell vertex formulation ‐ Multistage Time Stepping ‐ FDM ‐like finite volume techniques ‐ Central and up‐wind type discretization ‐ Treatment of derivatives. Lab experiments: ● Numerical simulation of turbulent flow past Airfoils on open source software ● Numerical structure analysis of a fuselage
Pressure and Velocity corrections ‐ Pressure correction equation; SIMPLE algorithm and its variants; PISO algorithms; Turbulence models – algebraic mixing length model, one and two equation models ‐ High and low Reynolds number models – Case study of Stage separation Aerodynamics of future space transport systems. Lab experiments: ● Numerical analysis of Composite laminated plate ● Numerical structural analysis of a landing gear
Reference Book:
1. J. D. Anderson, ―Computational Fluid Dynamics: The Basics with Applications‖, McGraw Hill Education, Indian Edition 2017 2. John F. Wendt (Editor), ―Computational Fluid Dynamics: An Introduction‖, A Von Karman Institute Book, 3rd Edition. 2009 3. K.. Muralidhar and T. Sundararajan (Editors), ―Computational Fluid Flow and Heat Transfer‖, 3 rd edition 4. Klaus A. Hoffmann and Steve T. Chiang, ―Computational Fluid Dynamics for Engineers‖, Vols. I, II and III, 4th 5. SedatBiringen and Chuen‐Yen Chow, ―An Introduction to Computational Fluid Mechanics by Example‖, 2nd Ed., John Wiley and Sons, New York, 2011
Text Book:
1. R.H. Pletcher, J.C. Tannehill, and D.A. Anderson, ―Computational Fluid Mechanics and Heat Transfer‖, 3rd Edition, CRC Press ‐ Taylor & Francis, 2013. 2. W. Versteeg and H. Malalasekara, ―An Introduction to Computational Fluid Dynamics: The Finite Volume Method‖, 2nd Edition, Pearson Education, 2010.
