Preprint 2002-047

Computation of Riemann Solutions Using the Dafermos Regularization and Continuation

Stephen Schecter, Bradley J. Plohr, and Dan Marchesin

Abstract: We present a numerical method, based on the Dafermos regularization, for computing a one-parameter family of Riemann solutions of a system of conservation laws. This family corresponds to varying either the left or right state of the Riemann problem. The Riemann solutions are required to have shock waves that satisfy the viscous profile criterion prescribed by the physical model. The method uses standard continuation software to solve a boundary-value problem in which the left and right states of the Riemann problem appear as parameters. Because the continuation method can proceed around limit point bifurcations, it can sucessfully compute multiple solutions of a particular Riemann problem, including ones that correspond to unstable solutions of the viscous conservation laws.



Paper:
Available as PostScript (1.3 Mbytes) or gzipped PostScript (240 Kbytes; uncompress using gunzip).
Author(s):
Stephen Schecter, <schecter@math.ncsu.edu>
Bradley J. Plohr, <plohr@ams.sunysb.edu>
Dan Marchesin, <marchesi@impa.br>
Publishing information:
Comments:
Submitted by:
<schecter@math.ncsu.edu> September 18 2002.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Thu Sep 19 08:13:24 MEST 2002