17ME651 Computational Fluid Dynamics syllabus for ME

Introduction to CFD and Governing Equations

Need of CFD as tool, role in R&D, continuum, material or substantial derivative or total derivative, gradient, divergence and curl operators, Linearity, Principle of Superposition. Derivation of Navier-Stokes equations in control volume (integral form) and partial differential form, Euler equations (governing inviscid equations). Mathematical classification of PDE (Hyperbolic, Parabolic, Elliptic). Method of characteristics, Introduction to Riemann Problem and Solution Techniques.

One-dimensional Euler's equation

Conservative, Non-conservative form and primitive variable forms of Governing equations. Flux Jacobian Is there a systematic way to diagonalise Eigenvalues and Eigenvectors of Flux Jacobian. Decoupling of Governing equations, introduction of characteristic variables. Relation between the two non-conservative forms. Conditions for genuinely nonlinear characteristics of the flux Jacobian. Introduction to Turbulence Modeling: Derivation of RANS equations and k-epsilon model.

Representation of Functions on Computer

Need for representation of functions, Box Function, Hat Function, Representation of sinx using hat functions: Aliasing, high frequency, low frequency. Representation error as a global error. Derivatives of hat functions, Haar functions, Machine Epsilon. Using Taylor series for representation of Derivatives.

Finite difference method –

Applied to Linear Convection equation, Laplace Equations, Convection Diffusion equations, Burgers equations, modified equations • Explicit methods and Implicit methods – as applied to applied to linear convection equation, Laplace equations, convectiondiffusion equation◦ FTCS, FTFS,FTBS,CTCS ◦ Jacobi Method, Gauss-Siedel, Successive Over Relaxation Method, TDMA.• VonNaumann stability (linear stability) analysis. Upwind Method in Finite Difference method.

Finite volume method

Finite volume method. Finding the flux at interface.

Central schemes -

Lax-Friedrichs Method, Lax-Wendroff Method, Two-Step Lax-Wendroff Method and Mac Cormack Method

Upwind Method in Finite Volume methods -

Flux Splitting Method Steger and Warming, vanLeer, Roe's Method and finding Roe's Averages.

Course outcomes:

• Understand mathematical characteristics of partial differential equations.
• Explain how to classify and computationally solve Euler and Navier-Stokes equations.
• Make use of the concepts like accuracy, stability, consistency of numerical methods for the governing equations.
• Identify and implement numerical techniques for space and time integration of partial differential equations.
• Conduct numerical experiments and carry out data analysis.
• Acquire basic skills on programming of numerical methods used to solve the Governing equations.

TEXT BOOKS:

1. T.j.chung,Computational Fluid Dynamics, , Cambridge University Press

2. Ghoshdastidar, Computational fluid dynamics and heat transfer, Cengage learning, 2017.

3. Charles Hirsch,Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics – Vol 1 &Vol 2, Butterworth- Heinemann, 2007

REFERENCE BOOKS

1. Pletcher, r. H., Tannehill, j. C., Anderson, d., Computational fluid mechanics and heat transfer, 3rd ed., Crc press, 2011, ISBN 9781591690375.

2. Moin, p., Fundamentals of engineering numerical analysis, 2nd ed., Cambridge university press, 2010, ISBN 9780521805261 (e- book available).

3. Ferziger, j. H., Numerical methods for engineering application, 2nd ed., Wiley, 1998.

4. Ferziger, j. H., Peric, m., Computational methods for fluid dynamics, 3rd ed., Springer, 2002.

5. Leveque, r., Numerical methods for conservation laws, lectures in mathematics, eth Zurich, birkhauser,199

6. Riemann Solvers and Numerical methods for Fluid Dynamics – A

7. Practical Introduction- Eleuterio F Toro, Springer Publications.