EML 5725 Computational Fluid Dynamics Spring 2003
Individual Project 1

There is no working together on this project. Upon suspicious similarities between projects, the F grade will be assigned to all parties involved. See the instructor with questions.

Write program that solve the following problem for the unknown velocity u(x,t):

Either Burgers' equation in nonconservative form:

or Burgers' equation in conservative form:

Assume the solution is periodic, i.e., for any x:

Initial condition:

where u₀ is a given constant.

Write the following three programs:

1.

The nonconservative first order upwind method:

Show that this scheme does not have the conservative property. Compute to time t=3 using, say, 64 points, and graphically compare numerical and exact solutions.

2.

The conservative first order ``upwind finite volume scheme''

where

Run the same case as the nonconservative scheme and comment whether using conservative schemes is necessary for schock capturing.

3.

The conservative second order MacCormack scheme. Run both the first order and the MacCormack scheme to time t=1.3 and comment whether the higher order scheme is better.

Use a maximum Courant number at each time step C=0.5 and use u₀=0.5.

Thoroughly discuss the results.

The usual notes on neatness and efficient and proper coding apply. See the required input file, exact solution, and example program in the supporting materials section