Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti

Hyperbolic systems with relaxation
Introduction
Many physical models are described by hyperbolic systems with relaxation of the form
∂tU + ∂xF (U) = 1
R(U), x ∈ R,
ε
where U = U(x, t) ∈ R N , F : R N → R N , F ′ (U) has real eigenvalues and admits a basis of
eigenvectors ∀ U ∈ R N and ε > 0 is called relaxation parameter.
Examples
Gas dynamics
Shallow water
Discrete kinetic models
Extended Thermodynamics
Hydrodynamical models for semiconductors
Traffic models
Granular gases
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Related problems: convection-diffusion-reaction, low Mach number/diffusive limits
⊲ Purpose of the talk is to give an overview of Runge-Kutta time discretization methods
for such systems, with particular emphasis on the treatment of stiff regimes.
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