Unit 1

Introduction to Numerical Methods – Properties of Numerical Solutions: Errors, Consistency, Accuracy, Stability, Convergence, Conservation – Review of Governing Equations of Fluid Dynamics – Review of Classification of PDE’s and their Physical Implications for Compressible Flows.

Unit 2

Introduction to the Finite Difference Methods: Discretization of Temporal and Spatial Derivatives, Explicit and Implicit Formulations – Mccormack’s Scheme, Extensions to Viscous Flows – Shock Capturing – Lax-Wendroff Method.

Unit 3

Stability Analysis: Von Neumann Stability Criteria, CFL Criterion for Stability – Introduction to Grid Generation: Body Conforming Grids, Algebraic and Elliptic Grids, 2D Unstructured Grids, C-Grids, O- Grids and H-Grids for Flow Past Airfoils and Wings – Simulation of External and Internal Flows as Applied to Aerospace Components.

Objectives

• The objective of the course is to introduce students to the finite difference method and related numerical techniques involved in the study of fluid flow problems.

Course Outcomes

• CO1: Recall the governing equation of fluid dynamics in conservation and non-conservation form.
• CO2: Utilize finite difference method for the discretization of the fluid flow problems.
• CO3: Make use of suitable numerical methods for solving the governing equations in the discretizied domain by understanding stability sand convergence.
• CO4: Choose proper structured / unstructured 2D grids specific to particular fluid flow problems.
• CO5: Apply the FDM to develop CFD techniques: Lax-Wendroff , MacCormack techniques.
• CO6: Experiment numerically the theoretical understanding of Computational Fluid Dynamics using software packages.

CO – PO Mapping

Textbook(s)

• John D Anderson, “Computational Fluid Dynamics – The Basics With Application”, Mcgraw-Hill, 1995.

Reference(s)

• T. J. Chung, “Computational Fluid Dynamics”, Cambridge University Press,2010.

Evaluation Pattern