Preprint 2001-002

A Class of Approximate Riemann Solvers and Their Relation to Relaxation Schemes

Randall J. LeVeque and Marica Pelanti


Abstract: We show that a simple relaxation scheme of the type proposed by Jin and Xin can be reinterpreted as defining a particular approximate Riemann solver for the original system of $m$ conservation laws. Based on this observation, a more general class of approximate Riemann solvers is proposed which allows as many as $2m$ waves in the resulting solution. These solvers are related to more general relaxation systems and connections with several other standard solvers are explored. The added flexibility of $2m$ waves may be advantageous in deriving new methods. Some potential applications are explored for problems with discontinuous flux functions or source terms.


Paper:
Available as PostScript (536 Kbytes) or gzipped PostScript (103 Kbytes; uncompress using gunzip).
Author(s):
Randall J. LeVeque, <rjl@amath.washington.edu>
Marica Pelanti, <pelanti@amath.washington.edu>
Publishing information:
J. Comput . Phys. 172 (2001), 573-591.
Comments:
Revised version received September 24
Submitted by:
<rjl@amath.washington.edu> January 15 2001.


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