Unit 1

Strong and Weak Form of Conservation of Equations – Introduction to Finite Volume Method: Discretization Schemes and their Properties for Finite Volume Method.

Unit 2

Finite Volume Method for Convection-Diffusion Problems: Central Differencing, Upwind Differencing, PowerLaw Differencing, Quick and TVD Schemes with their Assessments – Staggered and Collocated Grids – Introduction to Multigrids – Flux-Vector Splitting.

Unit 3

Introduction to Solution Algorithms: SIMPLE, SIMPLER, SIMPLEC and PISO Algorithms – Introduction to Turbulence Models and Associated Parameters – Introduction to Aerodynamic Shape Optimization – Introduction to Spectral Methods.

Course Objectives

• The objective of the course is to introduce students to the finite volume method and related advanced numerical techniques and algorithms.

Course Outcomes

• CO1: Understanding strong and weak form of governing equation and the basics of Finite Volume Method (FVM) to discretize partial differential equations.
• CO2: Applying FVM schemes like upwind, Center Difference, power-law, quick, TVD for convection-diffusion type problems and assess the schemes.
• CO3: Applying solution methodologies like SIMPLE, SIMPLER, SIMPLEC, PISO for staggered and collocated grids.
• CO4: Understanding Turbulence Models and Associated parameters.
• CO5: Understanding of advanced concepts: multigrids, flux-vector splitting, spectral methods, aerodynamic shape optimization.
• CO6: Numerically model the theoretical understanding of Computational Fluid Dynamics using open-source packages such as LAMMPS, Open Foam.

CO – PO Mapping

Textbook(s)

• Hirsch, “Numerical Computation of Internal and External Flows- Vol 1-2”, 2^nd edition, Elsevier, 2007.
• Veertseeg.H, Malalasekara.W, “An Introduction to Computational Fluid Dynamics- The Finite Volume Approach”, 2^nd edition, Pearson Education Limited, 2008.

Reference(s)

• T.J. Chung, “Computational Fluid Dynamics,” 2nd edition, Cambridge University Press, 2010.
• John Tannehill, Dale Anderson, Richard Pletcher, “Computational Fluid Mechanics and Heat Transfer,” 3^rd Edition, CRC Press, 2013.
• Canuto C., Hussaini M. Y., Quarteroni A., and Zang T.A., “Spectral Methods. Fundamentals in Single Domains.” Springer-Verlag, 2006.

Evaluation Pattern