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Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
Lorenzo Pareschi,Giovanni Russo +1 more
TLDR
In this article, new implicit-explicit (IMEX) Runge-Kutta methods were proposed for hyperbolic systems of conservation laws with stiff relaxation terms. But the implicit part is treated by a strong-stability-preserving (SSP) scheme, and the explicit part is represented by an L-stable diagonally implicit Runge Kutta method (DIRK).Abstract:
We 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.read more
Citations
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Numerical methods for kinetic equations
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Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure
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Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit
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A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics
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References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Journal ArticleDOI
Linear and Nonlinear Waves
G. B. Whitham,T. C. T. Ting +1 more
TL;DR: In this paper, a reference record was created on 2005-11-18, modified on 2016-08-08 and used for the purpose of ondes ; chocs ; onde de : choc reference record.
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