Computational Fluid Dynamics ChemE NPTEL

Description: Illustration of the CFD approach; CFD as an engineering analysis tool. Derivation of flow governing equations; turbulence modeling; modeling approaches for multiphase flow; initial and boundary conditions; wellposedness. Discretization of the governing equations using finite difference/volume/element methods; concepts of consistency, stability and convergence; template for the discretization of a generic unsteady transport equation. Solution of discretized equations; direct methods; classical iterative methods; advanced methods for structured matrices; conjugate gradient techniques; multigrid methods. Solution of coupled equations: methods for compressible flows; evaluation of pressure in incompressible flows; pressure-velocity coupling algorithms. Structured and unstructured grids; structured grid generation; unstructured grid generation.
Resources: OpenCourseware from NPTEL (India), Sheridan College, MIT, UC Berkeley, Stanford & many other of the World's finest University's.

Language: English

Professors: Michael Williams

Units: 47

Lesson content
Mod-01 Lec-01 Motivation for CFD and Introduction to the CFD approach
Mod-01 Lec-02 Illustration of the CFD approach through a worked out example
Mod-02 Lec-03 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation
Mod-02 Lec-04 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation
Mod-02 Lec-05 Forces acting on a control volume; Stress tensor;
Mod-02 Lec-06 Kinematics of deformation in fluid flow; Stress vs strain rate relation
Mod-02 Lec-07 Equations governing flow of incompressible flow;
Mod-03 Lec-08 Cut out the first 30s; Spatial discretization of a simple flow domain;
Mod-03 Lec-09 Finite difference approximation of pth order of accuracy for qth order derivative;
Mod-03 Lec-10 One-sided high order accurate approximations,Explicit and implicit formulations
Mod-03 Lec-11 Numerical solution of the unsteady advection equation using different finite.
Mod-03 Lec-12 Need for analysis of a discretization scheme; Concepts of consistency
Mod-03 Lec-13 Statement of the stability problem
Mod-03 Lec-14 Consistency and stability analysis of the unsteady diffusion equation
Mod-03 Lec-15 Interpretation of the stability condition,Stability analysis of the generic scalar equ
Mod-04 Lec-16 Template for the generic scalar transport equation and its extension to the solution
Mod-04 Lec-17 Illustration of application of the template using the MacCormack scheme
Mod-04 Lec-18 Stability limits of MacCormack scheme
Mod-04 Lec-19 Artificial compressibility method and the streamfunction-vorticity method
Mod-04 Lec-20 Pressur e equation method for the solution of NS equations
Mod-04 Lec-21 Pressure-correction approach to the solution of NS equations on a staggered grid
Mod-05 Lec-22 Need for efficient solution of linear algebraic equations
Mod-05 Lec-23 Direct methods for linear algebraic equations; Gaussian elimination method
Mod-05 Lec-24 Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm
Mod-05 Lec-25 Basic iterative methods for linear algebraic equations: Description of point -Jacobi
Mod-05 Lec-26 Convergence analysis of basic iterative schemes,Diagonal dominance condition
Mod-05 Lec-27 Application to the Laplace equation
Mod-05 Lec-28 Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting
Mod-05 Lec-29 Advanced iterative methods,Strongly Implicit Procedure,Conjugate gradient method
Mod-05 Lec-30 Illustration of the Multigrid method for the Laplace equation
Mod-06 Lec-31 Overview of the approach of numerical solution of NS equations for simple domains
Mod-06 Lec-32 Derivation of the energy conservation equation
Mod-06 Lec-33 Derivation of the species conservation equation; dealing with chemical reactions
Mod-06 Lec-34 Turbulence,Characteri stics of turbulent flow,Dealing with fluctuations
Mod-06 Lec-35 Derivation of the Reynolds -averaged Navier -Stokes equations
Mod-06 Lec-36 Reynol ds stresses in turbulent flow,Time and length scales of turbulence
Mod-06 Lec-37 One-equation model for turbulent flow
Mod-06 Lec-38 Two -equation model for turbulent flow; Numerical calculation of turbulent
Mod-06 Lec-39 Calculation of near-wall region in turbulent flow; wall function approach
Mod-07 Lec-40 Need for special methods for dealing with irregular fl ow geometry
Mod-07 Lec-41 Transformation of the governing equations; Illustration for the Laplace equation
Mod-07 Lec-42 Finite volume method for complicated flow domain
Mod-07 Lec-43 Finite volume method for the general case
Mod-07 Lec-44 Generation of a structured grid for irregular flow domain; Algebraic methods
Mod-07 Lec-45 Unstructured grid generation,Domain nodalization
Mod-07 Lec-46 Delaunay triangulation method for unstructured grid generation
Mod-07 Lec-47 Co -located grid approach for irregular geometries; Pressure correction equations