Computational Fluid Mechanics and Heat Transfer - II

AERE-547

Previous offerings

Spring 2023, Sp'22, '20

Course Objectives

In this course, the students learn computational techniques to solve fluid flow equations. The learning objectives are to understand and implement the following concepts in codes developed from scratch.

Outcomes

On completion of the course the attentive student will understand:

  • The governing fluid flow equations
  • Numerical error analysis: consistency, stability, and convergence of numerical
  • schemes; von Neumann, matrix method of error analysis, etc.,
  • Monotonicity, flux limiters, and total variation diminishing (TVD), MUSCL
  • schemes
  • Methods for the compressible Euler equations: shock capturing, flux-vector + splitting, flux-difference splitting, higher-order methods
  • Methods for incompressible flow: SIMPLE (R,C), PISO

Syllabus

  • Governing fluid flow equations: continuity, momentum, & energy:
    • The general form of a conservation law
    • Mass, momentum, and energy conservation laws
    • Conservation & non-conservation forms: integral & differential form
    • Transformation from physical to computational space
  • Dynamic levels of approximation of the Navier-Stokes system of equations
    • DNS, RANS, LES
    • Thin shear layer approximation
    • Parabolized N-S
    • Euler equations
    • Potential flow
  • Numerical error analysis
    • Consistency, stability, and convergence
    • von Neumann method for stability analysis
    • Spectral analysis of numerical error: dissipation, dispersion
    • Matrix method for stability
  • High-resolution numerical schemes
    • General formulation of numerical schemes with prescribed order of accuracy
    • Monotonicity of numerical schemes
    • Concept of flux limiters
    • TVD, MUSCL schemes
    • ENO/WENO schemes
  • Methods for the compressible Euler equations
    • Flux-vector splitting
    • Flux-difference splitting
    • Higher-order schemes
  • Methods for the N-S equations
    • Explicit & implicit methods
    • Hybrid schemes
    • Preconditioning for low Mach number flows
    • Incompressible N-S: SIMPLE, PISO, etc.
  • Project A: 2D shock wave propagation
  • Project B: Lid-driven cavity

Textbook and reading mtl.

The suggested reading materials include the following.

  • Hirsch, C. (2007). Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics. Elsevier.
  • Hirsch, C. (1990). Numerical computation of internal and external flows. Vol. 2: Computational methods for inviscid and viscous flows. John Wiley & Sons.
  • Pletcher, R. H., Tannehill, J. C., & Anderson, D. (2012). Computational fluid mechanics and heat transfer. CRC Press.
  • Patankar, S. (1980). Numerical heat transfer and fluid flow. CRC Press.
  • Toro, E. F. (2013). Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Science & Business Media.

Lecture videos