Course

Module 1

Review of Conservation equations for mass, momentum and energy; Equations in rectangular, cylindrical and spherical coordinate systems; Eulerian and Lagrangian approach, Conservative and non-conservative forms of the equations, rotating co-ordinates.
Classification of system of PDEs : parabolic elliptic and hyperbolic ; Boundary and initial conditions;
Numerical Grid Generation: Basic ideas, transformation and mapping, unstructured grid generation, hybrid grids,moving grids,unmatched meshes,CGNS notation forgrid and data,mesh-free calculations.

Module 2

Finite Volume Method: Basic methodology, finite volume discretization, approximation of surface and volume integrals, interpolation methods – Central, Upwind, Hybrid, Power Law and QUICK formulations and comparison for convection-diffusion problem;
TVD schemes, Flux limiter functions; Advanced Finite Volume methods: FV discretization in two and three dimensions,SIMPLE algorithm and flow field calculations, variants of SIMPLE- SIMPLER, SIMPLEC; PISO and PIMPLE algorithms.

Module 3

Turbulence and turbulence modeling, Introduction to turbulence modeling, Reynolds stress, RANS model, one-, two- and multiple equations for turbulence modeling; Reynolds Stress Transport Model; Large Eddy Simulation, Detached Eddy Simulation and Direct Numerical Simulation methods; Illustrative flow computations using CFD codes.
CFD methods for compressible and high-speed flows ;reacting flows.
Finite element methods: Introduction to Finite Element Analysis, formulation of finite element methods for heat transfer in solids, formulation of finite element methods for fluid flows:In compressible flows, Navier-Stokes equations including heat transfer.
Formulation for fluid-structure interactions:Moving mesh and adaptive mesh, acoustic fluids coupled to structures, Navier-Stokes fluids coupled to structures Commercial software–grid generation, flow prediction and post-processing. Validation methods for CFD analysis.
Introduction to open source CFD packages and solution to practical problems, Introduction to turbulence models.

Lab Session

• Solving 1D and 2D heat diffusion problem without heat generation using finite volume techniques using Python/Matlab.
• Solving 1D and 2D heat diffusion problem with heat generation using finite volume techniques using Python/Matlab.
• Solving unsteady 1D heat diffusion problem without heat generation using finite volume techniques using Python/Matlab.
• Simulate 2D incompressible laminar flow through a rectangular channel. Determine the velocity profile at various locations and compare with the analytical parabolic profile for Poiseuille flow using Ansys Fluent/OpenFOAM.

• CO1:Familiarization with conversation equations in different forms and ability to classify a system of PDEs.
• CO2: Apply FVM techniques for diffusion and convection-diffusion problems.
• CO3:Understand and apply different pressure-velocity coupling for incompressible flows.
• CO4:Numerical modeling of turbulence and ability to choose the most optimum one for a problem.
• CO5: Solution of compressible fluid flows and its applications .CO6:Usage of commercial and open source CFD codes.

• Versteeg,H. and Malalasekra, M.,An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2^nd, PrenticeHall. 2007
• Dale Anderson, JohnC.Tannehill, RichardH. Pletcher, Ramakanth Munipalli, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 4^thCRCPress,2021.
• Hirsch, Analysis of Internal and external flows,Vols1,2.Wiley-Jnterscience,2007
• Jaluria,Y., and Torrance, K.E., Computational Heat Transfer, Taylor & Francis.2002.
• Ferziger, JoelH., Peric, Milovan, Street,RobertL, Computational Methods for Fluid Dynamics,4th Ed. Springer. 2020.
• Bathe,K.J. Finite Element Procedures. 2^ndEd.Klaus-JurgenBathe,MIT,2014