Computational Fluid Dynamics and Heat Transfer

This course is an effort to cover a range of topics, - from elementary concepts for the uninitiated students to state-of-the-art algorithms useful for the practitioners. The contents begin with preliminaries, in which the basic principles and techniques of finite difference (FD), finite volume (FV) and finite element (FE) methods are described using detailed mathematical treatment. The methodologies are explained using step-by-step calculations. The popular CFD solvers, such as SIMPLE and MAC have been discussed in a detailed manner so that the learners can handle such programming paradigms with confidence.
INTENDED AUDIENCE:BTech (UG) in Mechanical. Chemical and Aerospace; MSc in Mathematics; MTech (PG) in Mechanical (Fluids and Thermal), MTech in Aerospace EngineeringPREREQUISITES: First and Second year Mathematics Courses. The basic core course in Fluid Mechanics and a basic core course in Heat TransferINDUSTRIES SUPPORT:DRDO Labs, Some CSIR Labs, BHEL, Thermax, GE etc

COURSE LAYOUT

Week 1:Introduction about the Course; Finite Difference Method (preliminaries); Explicit, Implicit, ADI FormulationWeek 2:Stability Analysis; Conservative and Transportive PropertiesWeek 3:Upwinding, Artificial Viscosity, Second Upwind; Higher order Upwinding and some Important IssuesWeek 4:Applications of Knowledge and Setting up an Algorithm; Finite Volume Method (FVM-preliminary concepts)
Week 5:FVM-Equations with First Derivatives; FVM-Equations with Second DerivativesWeek 6:Finite Element Method (FEM-Preliminary Concepts); FEM-Galerkin Weighted Residual MethodWeek 7:FEM-Elemental contributions and formation of Global Matrix; Vorticity Stream Function Approach (Formulation and Algorithm)Week 8:Vorticity Stream Function Approach (Application to Curvilinear Geometry); SIMPLE Algorithm (Continuity and Momentum Equations)
Week 9:SIMPLE Algorithm (Momentum Equations and Pressure Solver)MAC Algorithm (The MAC Method and Discretization of the Equations)Week 10:MAC Algorithm (Pressure - Velocity Iteration and the Solution);MAC Algorithm (Solution of Energy Equation)Week 11:A Finite Volume Method to solve NS Equations in 3D Complex GeometryWeek 12:FVM-3DC (Convective and Diffusive Fluxes);FVM-3DC (Solution for Pressure and the Algorithm);Mathematical Approaches to Turbulent Flows (Preliminaries and Modeling Framework / Modeling on the basis of RANS)