G. Russo
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit.
Fri, 10/21/2011 - 15:01 — SomNambulAuthors: L. Pareschi, G. Russo, S. Boscarino
Subjects: Numerical Analysis
AbstractWe consider Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic and
kinetic equations in the diffusion limit. In such regime the system relaxes
towards a parabolic convection-diffusion equation and it is desirable to have a
method that is able to capture the asymptotic behavior with an implicit
treatment of the limiting diffusive terms. To this goal we reformulate the
problem by properly combining the limiting diffusion flux with the convective
flux. This, however, introduces new difficulties due to the dependence of the
stiff source term on the gradient.Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation.
Thu, 09/16/2010 - 15:01 — SomNambulAuthors: L. Pareschi, G. Russo
Subjects: Numerical Analysis
AbstractWe consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic
systems of conservation laws with stiff relaxation terms. The explicit part is
treated by a strong-stability-preserving (SSP) scheme, and the implicit part is
treated by an L-stable diagonally implicit Runge-Kutta methods (DIRK). The
schemes proposed are asymptotic preserving (AP) in the zero relaxation limit.
High accuracy in space is obtained by Weighted Essentially Non Oscillatory
(WENO) reconstruction. After a description of the mathematical properties of
the schemes, several applications will be presented.
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