Abstract
The ability of Well-Balanced (WB) schemes to capture very accurately
steady-state regimes of non-resonant hyperbolic systems of
balance laws has been thoroughly illustrated since its introduction
by Greenberg and LeRoux (1996) [15] (see also the anterior WB
Glimm scheme in E, 1992 [8]). This paper aims at showing, by
means of rigorous C0
t (L1x
) estimates, that these schemes deliver an
increased accuracy in transient regimes too. Namely, after explaining
that for the vast majority of non-resonant scalar balance laws,
the C0
t (L1x
) error of conventional fractional-step (Tang and Teng,
1995 [45]) numerical approximations grows exponentially in time
like exp(max(g
)t)
?
x (as a consequence of the use of Gronwall's
lemma), it is shown that WB schemes involving an exact Riemann
solver suffer from a much smaller error amplification: thanks to
strict hyperbolicity, their error grows at most only linearly in time
(see also Layton, 1984 [30]). Numerical results on several testcases
of increasing difficulty (including the classical LeVeque-Yee's
benchmark problem (LeVeque and Yee, 1990 [34]) in the non-stiff
case) confirm the analysis.
Anno
2013
Autori IAC
Tipo pubblicazione
Altri Autori
Debora Amadori amp; Laurent Gosse
Editore
Elsevier.
Rivista
Journal of differential equations (Print)