Unit 1

Introduction to Numerical Techniques: Numerical Methods – Round off and truncation errors – Approximations – Order of Convergence – Numerical interpolation. Application of concepts: Modelling friction in flows within constrained geometries – Generation of aerofoil geometries – Computation of a projectile trajectory

Unit 2

Solution techniques of a linear system of equations: Gauss elimination – Gauss-Jordan method– LU Decomposition – Iterative methods for linear systems. Solution of non-linear equations: Optimisation & NewtonRaphson methods. Application of concepts: Response of multi degree of freedom systems – Panel Method for Aerofoils – Optimisation of a parachute production cost.

Unit 3

Computational methods for ODEs: Eigen values – Single step methods – multi-step methods. Stability, consistency, accuracy and efficacy of these methods. Application of concepts: Dynamics of the linear simple pendulum – Dynamics of the non-linear simple pendulum – Modelling heat dissipation in turbine blades – Modelling the flow over flat plate geometry.

Course Objectives

• The objective of the course is to introduce students to the numerical techniques commonly used in solving engineering problems

Course Outcomes

• CO1: Given an engineering problem, understand the mathematical model required to describe the problem.
• CO2: Comprehend the physics represented by the mathematical model to select an appropriate method/algorithm.
• CO3: Apply the numerical solution method via a well-designed computer program.
• CO4: Analyse the numerical solutions that were obtained in regards to their accuracy and suitability for applications.

CO – PO Mapping

Textbook(s)

• S. C. Chapra, and R. P. Canale. Numerical methods for engineers. Boston: McGraw-Hill Higher Education, 2010.

Reference(s)

• S. P. Venkateshan, and P. Swaminathan. Computational methods in engineering. Elsevier, 2013.
• R. H. Landau, M. J. Paez and C. C. Bordeianu, Computational Physics -Problem Solving with Computers, WileyVCH, 2001.

Evaluation Pattern