## Course Detail

 Course Name Computational Fluid Dynamics Course Code 15MEC248 Program B. Tech. in Mechanical Engineering Year Taught 2019

### Syllabus

##### Unit 1

Introduction & conservation laws of fluid motion: Models of the fluid flow, Substantial derivative, Divergence of the velocity, Laws of Conservation – Continuity Equation, momentum Equation, Energy Equation, Dimensionless forms of Equations, Simplified Mathematical Model, Mathematical Classification of flows, Physical Boundary conditions.

Basics of numerics: Components of the Numerical solution Methods – Mathematical model, Discretization method, Co-ordinates and Basic Vector systems, Numerical Grid, Finite approximations, Solution Method, Convergence criteria. Properties of Numerical Solution Methods – Consistency, Stability, Convergence, Conservativeness, Boundedness, Realizability. Discretization Approaches – FEM, FDM, FVM.

##### Unit 2

Finite difference method: Approximation of the first Derivative – Taylor series expansion, Polynomial Fitting, Compact Schemes, Non-Uniform Grids. Approximation of the second derivative, Approximation of the mixed derivative, Explicit and Implicit approaches, Errors and Analysis of stability.

Spectral analysis and grid generation: Spectral Analysis of numerical Schemes, Higher order methods, High accuracy compact schemes. General transformation of the equations, Matrics and Jacobians, Stretched grids, Boundary fitted Coordinate systems, Elliptic grid generation, unstructured grids.

##### Unit 3

Computational heat transfer: Steady one & two dimensional heat conduction, Unsteady one-dimensional heat conduction, over-relaxation and under-relaxation. One dimensional steady convection and Diffusion.

Computational Fluid Flow: Solution methods for incompressible flows – collocated and staggered grid, Pressure correction equations, SIMPLE and SIMPLER Algorithm. Examples in simple geometries such as flow in channel, lid driven cavity flow and validation. Solution methods for compressible flows – Importance of conservation and upwinding. Simple artificial dissipation methods, pressure-correction methods for arbitrary Mach numbers. Applications to inviscid compressible flows.

### Text Books

• Ferziger J. H. and Peric M. – ‘Computational Methods for Fluid Mechanics’ – Springer – 2013 – 3rd Edition.
• Anderson J. D. – ‘Computational Fluid Dynamics: The Basics with applications’ – McGraw Hill – 2007

### Resources

• Sengupta T. K. – ‘Fundamentals of Computational Fluid Dynamics’ – Universities Press – 2004
• Patankar S. V. – ‘Numerical Heat transfer and Fluid Flow’ – Taylor & Francis Publications – 1980

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