Mechanical Engineering 424, Computational Fluid Dynamics I, II

Home  >  Courses  >  ME424

Catalog description

First Quarter: Navier-Stokes equations, velocity potential formulation, and stream function formulation. Computer implementation of numerical methods for ideal flow and acoustic approximations. Fast elliptic solvers. Second Quarter: Computer implementation of numerical methods for solution of nonlinear problems. Conservation equations (Lagrangian, Eulerian Arbitrary, Lagrangian-Eulerian). Stokes flows, advection diffusion equations, compressive flow, and fluid-structure interaction.

Prerequisite: None.

Who takes it

This course is usually taken by graduate students interested in computational methods for fluid flow problems. Undergraduates may also take 424-1 as an elective.

What it's about

Computational fluid dynamics is an important tool to investigate fluid flow problems in industry and academia. The first course in the series can be taken without prior background in computational techniques. A background of fundamental fluid dynamics, partial differential equations, linear algebra and a programming language is desirable. The primary focus in the first course is to gain a solid foundation of numerical methods for convection-diffusion problems. The emphasis is on the physical meaning underlying the required mathematics. A control volume method, which is a robust physically intuitive numerical approach, widely used in industry and academia alike, is taught in the first quarter. The second course focuses on advanced topics.

Lectures:

The class meets three times a week for 50 minutes lectures. An outline for 424-1 is given below:

  • Introduction:
    • Computational Fluid Dynamics (CFD) - a research, modeling and design tool
    • Historical perspective, commercial CFD packages, mathematical description of physical phenomena, a brief discussion of discretization methods - finite difference
    • Finite element, control volume methods
    • Introduction to control volume method - the focus of this course
  • Numerical solution of diffusion-type equations:
    • Steady one-dimensional conduction
    • Unsteady one-dimensional conduction
    • Two and three-dimensional situations
  • Numerical solution of convection-diffusion-type equations:
    • Steady one-dimensional convection-diffusion
    • Discretization equation in two and three-dimensions
  • Numerical solution of fluid flow equations:
    • Discretization of continuity and momentum equations for fluid flow
    • Pressure-based algorithms - SIMPLE & SIMPLER

Assessment/Evaluation:

Homework, a term project and in-class exams.

Textbook:

Suhas V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp., 1980.

Contact:

Professor: Neelesh Patankar
e-mail: n-patankar@northwestern.edu