PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise

Journal Article · Sat Jun 01 04:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.02.009· OSTI ID:22233591

Abdulle, Assyr ^[1]; Vilmart, Gilles ^[2]

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1. Mathematics Section, École Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne (Switzerland)
2. École Normale Supérieure de Cachan, Antenne de Bretagne, INRIA Rennes, IRMAR, CNRS, UEB, Av. Robert Schuman, F-35170 Bruz (France)

A partitioned implicit–explicit orthogonal Runge–Kutta method (PIROCK) is proposed for the time integration of diffusion–advection–reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.

• OSTI ID: 22233591
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 242; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ADVECTION
ALGORITHMS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
EFFICIENCY
ERRORS
FLEXIBILITY
NOISE
PARTITION
STOCHASTIC PROCESSES