CAE331 Numerical Methods in Fluid Dynamics Syllabus:
CAE331 Numerical Methods in Fluid Dynamics Syllabus – Anna University Regulation 2021
COURSE OBJECTIVES
• To make students understand the complexity of general fluid dynamic equations in partial differential form in the mathematical nature of the equations.
• To make students understand the complexity of general fluid dynamic equations under different flow conditions
• To impart knowledge to students on the basic aspects of finite differences and finite volume methods
• To impart knowledge to students on the basic aspects of finite element methods
• To expose the students on obtaining solutions for a set of a large number of algebraic equations using the panel methods as examples and to trin them to obtain numerical solutions for steady supersonic flows
UNIT-I MATHEMATICAL NATURE OF FLUID DYNAMIC EQUATIONS
Governing equations of fluid dynamics and modelling of fluid flow – Eulerian and Lagrangian approaches – Mathematical nature of fluid dynamic equations – Classification of partial differential equations – General behavior of different classes of fluid dynamic equations – Practical examples of fluid dynamic problems governed by different classes of partial differential equations – ill posed and well posed problems
UNIT-II BOUNDARY CONDITIONS AND CHOICE OF NUMERICAL SCHEMES
Importance of boundary conditions in obtaining the numerical solution of fluid dynamic equations Types of boundary conditions- Boundary conditions for momentum equations for viscous and inviscid flows – Boundary conditions for energy equation for different flow conditions – Practical examples – Symmetry and cyclic boundary conditions – Stability of numerical solution and the choice of numerical schemes for different classes of fluid dynamic equations
UNIT-III INTRODUCTION TO FDM, FVM AND FEM
Introduction to finite difference, finite volume and finite element methods and their areas of application-A brief description of implementing methodologies for finite difference method, finite volume method and finite element method – Illustration of the methods using simple one dimensional fluid dynamic problems – Advantages and limitations of these methods
UNIT-IV PANEL METHODS
A brief description of source, sink and vortex flows – Application of panel methods – Methodology involved in implementing panel methods – Source panel method and its implementation – Solution methods for solving a set of large number of algebraic equations and their applications for panel methods – Solution example of flow over a circular cylinder – Vortex panel method and its implementation – Vortex lattice method
UNIT-V NUMERICAL METHODS FOR STEADY SUPERSONIC FLOWS
Two dimensional irrotational flow – Method of characteristics – Numerical methodology to obtain solution using method of characteristics for supersonic inviscid flows – Supersonic nozzle design using method of characteristics – Application of method of characteristics for axisymmetric irrotational flows – Description of Mc. Cormack’s Predictor-corrector technique – Shock capturing and shock fitting techniques
COURSE OUTCOMES:
CO1: will be able to understand the importance of numerical methods in finding solutions to complex engineering flow problems
CO2: will be able to develop interest in lifelong learning on numerical methods and apply the knowledge for the solution of aerospace related fluid dynamic problems
CO3: will acquire basic knowledge to learn modern engineering tools such as CFD software tools to solve and analyse the flow fields over the airplanes
CO4: will be able to apply skills to develop algorithms for the solutions of inviscid supersonic flow problems pertaining to aerospace field
CO5: will be able to create new computational techniques in computational methods such as FVM using the imparted knowledge
TEXT BOOKS:
1. Fletcher C.A.J. , “Computational Techniques for Fluid Dynamics 1” Springer Verlag, 1996. 118
2. Fletcher C.A.J., “Computational Techniques for Fluid Dynamics 2”, Springer Verlag, 1995.
REFERENCES:
1. Chung T. J., “Computational Fluid Dynamics”, Cambridge University Press; 2nd edition, 2010.
2. Hirsch C., “Numerical Computation of Internal and External Flows” Volume-2, John Wiley and Sons, 1994.
3. Joel H. Ferziger & Milovan Peric, “Computational Methods for Fluid Dynamics” Springer; 3rd edition 2002.
4. John F Wendt , “Computational Fluid Dynamics – An Introduction”, 3rd Edition, SpringerVerlag, Berlin Heidelberg, 2009.
5. Versteeg H.K. and Malalsekera W. “An Introduction to Computational Fluid Dynamics, The Finite Volume Method”, PHI; 2nd edition 2007.