Operator splitting methods with error estimator and adaptive time-stepping. Application to the simulation of combustion phenomena

Stéphane Descombes (1) , Max Duarte (2, 3) , Marc Massot (4, 5, 6)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
2 CCSE - Center for Computational Sciences and Engineering [LBNL Berkeley]
3 CD-adapco [London]
4 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
5 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
6 CentraleSupélec

Operator splitting techniques were originally introduced with the main objective of saving computational costs. A multi-physics problem is thus split in subproblems of different nature with a significant reduction of the algorithmic complexity and computational requirements of the numerical solvers. Nevertheless, splitting errors are introduced in the numerical approximations due to the separate evolution of the split subproblems and can compromise a reliable reproduction of the coupled dynamics. In this chapter we present a numerical technique to estimate such splitting errors on the fly and dynamically adapt the splitting time steps according to a user-defined accuracy tolerance. The method applies to the numerical solution of time-dependent stiff PDEs, illustrated here by propagating laminar flames investigated in combustion applications.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Milieux fluides et réactifs

Stéphane Descombes, Max Duarte, Marc Massot. Operator splitting methods with error estimator and adaptive time-stepping. Application to the simulation of combustion phenomena. Roland Glowinski; Stanley Osher; Wotao Yin. Splitting Methods in Communication, Imaging, Science, and Engineering, Springer International Publishing, pp.1-13, 2015, 78-3-319-41589-5. ⟨10.1007/978-3-319-41589-5⟩. ⟨hal-01183745v2⟩