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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