# AER1319: Finite-Volume Methods for CFD

Instructor: Professor C. P. T. Groth

University of Toronto Institute for Aerospace Studies (UTIAS)

Phone: (416) 667-7715

E-mail: groth@utias.utoronto.ca

Home page:
http://arrow.utias.utoronto.ca/~groth/

Course URL:
http://arrow.utias.utoronto.ca/~groth/aer1310

## Course Description

Introduction to upwind finite-volume methods widely used in
computational fluids dynamics (CFD) for thehe solution of
high-speed inviscid and viscous compressible flows. Topics
include:

**Brief review of conservation equations for compressible flows**;
Euler equations; Navier-Stokes equations; one- and two-dimensional forms;
model equations. **Mathematical properties of the Euler equations**;
primitive and conserved solution variables; eigensystem analysis;
compatibility conditions; characteristic variables, Rankine-Hugoniot conditions and
Riemann invariants; Riemann problem and exact solution. **Godunov's method**;
hyperbolic flux evaluation and numerical flux functions; solution
monotonicity; Godunov's theorem. **Approximate Riemann solvers**; Roe's
method. **Higher-order Godunov-type schemes**; semi-discrete form; solution
reconstruction including least-squares and Green-Gauss methods; slope
limiting. **Extension to multi-dimensional flows**. **Elliptic flux
evaluation for viscous flows**; diamond-path and average-gradient stencils;
discrete-maximum principle. **High-order methods**; essentially
non-oscillatory (ENO) schemes.

## Lectures - Fall Term

**Mondays**, 10:00 am - 12:00 pm, UTIAS Lecture Hall,
September 10 - December 17, 2018.

## Lectures - Spring Term

**Mondays**, 10:00 am - 12:00 pm, UTIAS Lecture Hall,
January 7 - April 29, 2019.

## Lecture Notes

Supplemental lecture notes will be provided for some of the subjects covered in the course.

## Additional Reading Material

A number of relevant papers are provided as additional reading for the course both to provide background, history, and perspective of finite-volume methods, as well as to act as a source of additional information. This additional reading material can be found here.

## Assignments

There will be six programming assignments given throughout the course. They are as follows:

**Assignment #1**: Due: Monday, ??.**Assignment #2**: Due: Monday, ??.**Assignment #3**: Due: Monday, ??.**Assignment #4**: Due: Monday, ??.**Assignment #5**: Due: Monday, ??.**Assignment #6**: Due: Monday, ??.

## Marks

The final grade will be based on marks obtained for the programming assignments.