Get 20% off all career paths from fullstack to AI
Earn Your Business Degree, Tuition-Free, 100% Online!
Overview
Google, IBM & Meta Certificates — All 10,000+ Courses at 40% Off
One annual plan covers every course and certificate on Coursera. 40% off for a limited time.
Get Full Access
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 departmentsPREREQUISITES: Fluid Mechanics, Thermodynamics, Engineering MathematicsINDUSTRY SUPPORT: HAL, NAL, ISRO, DRDO and Private Automobile and Aerospace Industries (Airbus, Boeing, Tata Motors etc.)
Syllabus
Week 1: Review of Thermodynamics & Fluid Mechanics
Week 2:Compressible flows and Isentropic relations
Week 3:Normal and Oblique Shock Waves
Week 4:Quasi-1D Flow and Nozzle Dynamics
Week 5:Hyperbolic Systems and Conservation Laws
Week 6:Basic Discretization Methods
Week 7:Numerical Methods for Conservation Laws
Week 8:Riemann Solvers
Week 9:Shock-Capturing and TVD Methods
Week 10:Finite Volume Method
Week 11:Boundary Treatments and Solver Development
Week 12:Applications and Advanced topics
- 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 (1st and 2nd 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
Taught by
Prof. Rajesh Ranjan, Prof. Niranjan Sahoo