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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Theorem guarantees that in the stiff limit the numerical scheme becomes the explicit<br />
RK scheme applied to the equilibrium system, and there<strong>for</strong>e the order of accuracy of the<br />
limiting scheme is greater or equal to the order of accuracy of the original IMEX scheme.<br />
In particular this implies that if the explicit part of the IMEX scheme is SSP then, in<br />
the stiff limit, we will obtain an SSP method <strong>for</strong> the limiting conservation law. This<br />
asymptotic SSP property is essential to avoid spurious oscillations in the limit scheme <strong>for</strong><br />
the limiting system of conservation laws.<br />
We recall that if U n represents a vector of solution values (<strong>for</strong> example obtained from a<br />
method of lines approach) we recall the following<br />
Definition 2 A sequence {U n }n∈N is said to be strongly stable in a given norm ||·|| provided<br />
that ||U n+1 || ≤ ||U n || <strong>for</strong> all n ≥ 0.<br />
The most commonly used norms are the T V -norm and the infinity norm.<br />
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