TY - JOUR
T1 - Quinpi: Integrating Stiff Hyperbolic Systems with Implicit High Order Finite Volume Schemes
AU - Puppo , Gabriella
AU - Semplice , Matteo
AU - Visconti , Giuseppe
JO - Communications in Computational Physics
VL - 1
SP - 30
EP - 70
PY - 2024
DA - 2024/07
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0199
UR - https://global-sci.org/intro/article_detail/cicp/23296.html
KW - Implicit methods, essentially non-oscillatory schemes, finite volumes, hyperbolic systems, entropy indicators.
AB - <p style="text-align: justify;">Many interesting physical problems described by systems of hyperbolic
conservation laws are stiff, and thus impose a very small time-step because of the
restrictive CFL stability condition. In this case, one can exploit the superior stability
properties of implicit time integration which allows to choose the time-step only from
accuracy requirements, and thus avoid the use of small time-steps. We discuss an efficient framework to devise high order implicit schemes for stiff hyperbolic systems
without tailoring it to a specific problem. The nonlinearity of high order schemes, due
to space- and time-limiting procedures which control nonphysical oscillations, makes
the implicit time integration difficult, e.g. because the discrete system is nonlinear also
on linear problems. This nonlinearity of the scheme is circumvented as proposed in
(Puppo et al., Comm. Appl. Math. &amp; Comput., 2023) for scalar conservation laws,
where a first order implicit predictor is computed to freeze the nonlinear coefficients of
the essentially non-oscillatory space reconstruction, and also to assist limiting in time.
In addition, we propose a novel conservative flux-centered a-posteriori time-limiting
procedure using numerical entropy indicators to detect troubled cells. The numerical
tests involve classical and artificially devised stiff problems using the Euler’s system
of gas-dynamics.</p>