Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
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Conclusions<br />
<strong>Runge</strong>-<strong>Kutta</strong> IMEX <strong>schemes</strong> represent a powerful tool <strong>for</strong> the time discretization of <strong>hyperbolic</strong><br />
<strong>systems</strong> with relaxation. In combination with finite volume <strong>schemes</strong> (up to second<br />
order) or finite difference <strong>schemes</strong> (of any order) they provide a new class of efficient<br />
underresolved <strong>schemes</strong> <strong>for</strong> the accurate solution of <strong>hyperbolic</strong> conservation laws with stiff<br />
source terms.<br />
Open problems and extensions:<br />
◦ 4th and 5th order IMEX-SSP <strong>schemes</strong><br />
◦ Higher order (more than third) finite volume <strong>schemes</strong> <strong>for</strong> <strong>hyperbolic</strong> <strong>systems</strong> with<br />
stiff relaxation<br />
◦ Less restrictive conditions <strong>for</strong> APk property<br />
◦ Development of well-balanced <strong>schemes</strong> that avoid numerical viscosity<br />
◦ Adaptive multi-modelling<br />
◦ Coupling with hybrid Monte Carlo strategies <strong>for</strong> multiscale problems.<br />
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