Course
UndergraduateSemester
ElectivesSubject Code
AE498Subject Title
Computational Methods for Compressible FlowsSyllabus
Basic equations – Hierarchy of mathematical models – Mathematical nature of flow equations and boundary conditions – Finite difference and finite volume methods – Analysis of Schemes: Numerical errors, stability, numerical dissipation – Grid generation – Wave equation – Numerical Solution of Compressible Euler Equation: Discontinuities and entropy, mathematical properties of Euler equation – Reconstruction-evolution – Upwind methods – Boundary conditions – Numerical solution of compressible Navier-Stokes equations – Turbulence Modeling: RANS, LES, DNS – Higher-order methods – Uncertainty in CFD: Validation and verification.
Text Books
Same as Reference
References
1. Hirsch, C., Numerical Computation of Internal and External Flows, Vol. I & II, Wiley (1998).
2. Laney, C. B., Computational Gasdynamics, Cambridge Univ. Press (1998).
3. LeVeque, R. J., Numerical Methods for Conservation Laws, 2nd ed., Birkhauser (2005).
4. Hoffmann, K. A. and Chiang, S. T., Computational Fluid Dynamics for Engineers, Vol. I, II & III, Engineering Education Systems (2000).
5. Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Intro- duction, 3rd ed., Springer (2009).
6. Blazek, J., Computational Fluid Dynamics: Principles and Applications, 2nd ed., Elsevier (2006).
7. Roache, P. J., Fundamentals of Verification and Validation, Hermosa Publishers (2009).
Course Outcomes (COs):
CO1: Discretize a partial differential equation (PDE), and recognize the type of PDE.
CO2: Formulate finite-difference and finite-volume schemes of the necessary order (spatial and temporal discretization).
CO3: Choose the finite-difference/finite-volume method and the number of boundary conditions based on the type of PDE.
CO4: Understand the various discretization errors and their implications for the outcome.
CO5: Learn about iterative procedures and error damping using iterative strategies.
CO6: Develop conventional second-order finite-volume algorithms using limiters.
CO7: Use advanced CFD tools to evaluate complex fluid-flow systems.