Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation
By Lorenzo Pareschi, Giovanni Russo. 2010
573 citations recorded by the source corpus.
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 method (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.
Subfields: Atmospheric Science, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/656845cc6b47334f5c47c03aea95ba1dbbec8735
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atmospheric Science
- Christopher A. Kennedy
- Mark H. Carpenter
- Giacomo Dimarco
- Lorenzo Pareschi
- J. McKinney
- Sergio Pirozzoli
In Computational Mechanics
- A. Tchekhovskoy
- Giacomo Dimarco
- Lorenzo Pareschi
- Mark H. Carpenter
- A. Sa̧dowski
- Christopher A. Kennedy
- Harvard
- J. McKinney
Citations in the corpus
- Strong stability of singly-diagonally-implicit Runge--Kutta methods (2008, unknown): “[2,5,27].”
- Numerical methods for kinetic equations* (2014, methodology): “We refer to Ascher et al. (1997), Kennedy and Carpenter (2003) and Pareschi and Russo (2005) for details.”
- Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review (2016, methodology): “They may also represent the implicit portion of an additive implicit-explicit (IMEX) method [25,44,47,48,83,160,164,200,205,255,289,334,337,356,460,461,468] or be used toward the solution of boundary value problems [99].”
- Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure (2013, methodology): “We use a set of IMEX coefficients that generates so-called strongly stable preserving (SSP) (formally known as total variational diminishing (TVD)) schemes (Pareschi & Russo 2000, 2005), such that the total variation in Uq always diminishes.”