Computational Gas Dynamics

By Prof. Rajesh Ranjan, Prof. Niranjan Sahoo | IIT Kanpur, IIT Guwahati

Learners enrolled: 792 | Exam registration: 114

ABOUT THE COURSE:

This course provides a comprehensive study of gas dynamics and its computational modeling, focusing on high-speed compressible flows. The first part of the course builds the foundation by covering the physics of shock waves, expansion fans, nozzle flows, and quasi-one-dimensional theory. The second part introduces numerical methods to solve the governing equations of compressible flow using shock-capturing schemes and Riemann solvers in finite difference and finite volume frameworks. Students will learn to implement basic and advanced discretization techniques and simulate practical problems such as shock tubes.

INTENDED AUDIENCE: UG and PG students in Mechanical/Aerospace engineering departments

PREREQUISITES: Fluid Mechanics, Thermodynamics, Engineering Mathematics

INDUSTRY SUPPORT: HAL, NAL, ISRO, DRDO and Private Automobile and Aerospace Industries (Airbus, Boeing, Tata Motors etc.)

Summary

Course Status :	Ongoing
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Aerospace Engineering Mechanical Engineering Computational Thermo Fluids Propulsion
Credit Points :	3
Level :	Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	02 Feb 2026
Exam Registration Ends :	20 Feb 2026
Exam Date :	19 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Review of Thermodynamics & Fluid Mechanics

Governing laws: mass, momentum, energy conservation
Thermodynamic relations for ideal gases
Speed of sound and Mach number
Classification of flows: Incompressible, compressible, subsonic, supersonic

Week 2: Compressible flows and Isentropic relations

Steady 1D and quasi-1D flow equations
Isentropic flow relations
Area-Mach number relation
Isentropic flow through nozzles

Week 3: Normal and Oblique Shock Waves

Normal shock relations and properties
Oblique shock theory and θ–β–M relation
Prandtl-Meyer expansion fans
Shock-expansion theory

Week 4: Quasi-1D Flow and Nozzle Dynamics

Flow with friction (Fanno flow) and heat addition (Rayleigh flow)
Analysis of converging and converging-diverging (C-D) nozzles

Week 5: Hyperbolic Systems and Conservation Laws

Properties of hyperbolic PDEs
Characteristics, eigenvalues, and wave speeds
Integral, Conservation and Characteristic forms
Advection and Diffusion Equations
Burgers' Equations
Euler equations in 1D and 2D

Week 6: Basic Discretization Methods

Finite difference methods: Taylor series approach
Central difference schemes (1^st and 2^nd order)
Upwind schemes: first-order upwind
Consistency, stability, and convergence
CFL condition

Week 7: Numerical Methods for Conservation Laws

Lax-Friedrichs, Lax-Wendroff, MacCormack methods
Concept of total variation and oscillations
Flux Splitting Methods

Week 8: Riemann Solvers

Riemann problem for hyperbolic systems
Exact vs. approximate Riemann solvers
Godunov's method and its limitations
Roe's approximate Riemann solver
HLL and HLLC solvers

Week 9: Shock-Capturing and TVD Methods

Nonlinear instability and need for limiters
Total Variation Diminishing (TVD) schemes
Flux and slope limiters (minmod, superbee, van Leer)
Entropy fix

Week 10: Finite Volume Method

Finite volume formulation
MUSCL scheme and slope reconstruction
Flux calculation and reconstruction
Multidimensional extension to 2D Euler equations

Week 11: Boundary Treatments and Solver Development

Reflective, inflow/outflow, wall boundaries
Characteristic boundary conditions
1D and 2D Euler solvers

Week 12: Applications and Advanced topics

Numerical simulation of shock tube
Oblique shock and expansion fan simulations
Verification and validation of CFD codes
Brief intro to Navier-Stokes solvers

Books and references

1. John D. Anderson Jr (1990), Modern Compressible Flow with Historical Perspective, McGraw-Hill, Singapore
2. J. John and T. Keith (2010), Gas Dynamics. 3^RD Edition, Pearson, New Delhi
3. Laney, B., Computational Gas Dynamics.
4. Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics.

Instructor bio

Prof. Rajesh Ranjan

IIT Kanpur

Dr. Rajesh Ranjan is an Assistant Professor in the Department of Aerospace Engineering at IIT Kanpur. He holds an M.E. from IISc Bengaluru and a Ph.D. from JNCASR Bengaluru. Prior to joining IIT Kanpur, he was a Postdoctoral Research Fellow at The Ohio State University and worked in the industry at Tata Computational Research Labs, Pune. His research interests lie in computational fluid dynamics, with applications in turbomachinery aerothermodynamics, high-speed flows, unsteady aerodynamics, and transition to turbulence. At IIT Kanpur, he has designed and taught several UG and PG courses, and has been recognized thrice with the Director’s Commendation for Outstanding Teaching.

Prof. Niranjan Sahoo

IIT Guwahati

Dr. Niranjan Sahoo is a Professor in the Department of Mechanical Engineering at IIT Guwahati. He received his Ph.D. from the Department of Aerospace Engineering at IISc Bangalore, following his B.Tech. in Mechanical Engineering. With over 16 years of teaching and research experience, he has taught a wide range of undergraduate and postgraduate courses in fluid and thermal sciences, including Fluid Mechanics, Thermodynamics, Heat and Mass Transfer, Combustion, and Gas Dynamics. Dr. Sahoo has actively contributed to interdisciplinary education through NPTEL courses, virtual labs, and TEQIP short-term training programs. He has supervised 15 Ph.D. students and published over 100 research papers in reputed journals and conferences. His research spans a broad range of topics in fluid mechanics, heat transfer, and propulsion.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: April 19, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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