This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady problems. The strategy considers a second-order Strang method and another lower order embedded splitting scheme that takes into account potential loss of order due to the stiffness featured by time-space multi-scale phenomena. The scheme is then built upon a precise numerical analysis of the method and a complementary numerical procedure, conceived to overcome classical restrictions of adaptive time stepping schemes based on lower order embedded methods, whenever asymptotic estimates fail to predict the dynamics of the problem. The performance of the method in terms of control of integration errors is evaluated by numerical simulations of stiff propagating waves coming from nonlinear chemical dynamics models as well as highly multi-scale nanosecond repetitively pulsed gas discharges, which allow to illustrate the method capabilities to consistently describe a broad spectrum of time scales and different physical scenarios for consecutive discharge/post-discharge phases.
Stéphane Descombes 1 ; Max Duarte 1 ; Thierry Dumont 1 ; Violaine Louvet 1 ; Marc Massot 1
@article{CML_2011__3_3_413_0,
author = {St\'ephane Descombes and Max Duarte and Thierry Dumont and Violaine Louvet and Marc Massot},
title = {Adaptive time splitting method for multi-scale evolutionary partial differential equations},
journal = {Confluentes Mathematici},
pages = {413--443},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {3},
number = {3},
year = {2011},
doi = {10.1142/S1793744211000412},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744211000412/}
}
TY - JOUR AU - Stéphane Descombes AU - Max Duarte AU - Thierry Dumont AU - Violaine Louvet AU - Marc Massot TI - Adaptive time splitting method for multi-scale evolutionary partial differential equations JO - Confluentes Mathematici PY - 2011 SP - 413 EP - 443 VL - 3 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744211000412/ DO - 10.1142/S1793744211000412 LA - en ID - CML_2011__3_3_413_0 ER -
%0 Journal Article %A Stéphane Descombes %A Max Duarte %A Thierry Dumont %A Violaine Louvet %A Marc Massot %T Adaptive time splitting method for multi-scale evolutionary partial differential equations %J Confluentes Mathematici %D 2011 %P 413-443 %V 3 %N 3 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744211000412/ %R 10.1142/S1793744211000412 %G en %F CML_2011__3_3_413_0
Stéphane Descombes; Max Duarte; Thierry Dumont; Violaine Louvet; Marc Massot. Adaptive time splitting method for multi-scale evolutionary partial differential equations. Confluentes Mathematici, Tome 3 (2011) no. 3, pp. 413-443. doi : 10.1142/S1793744211000412. https://cml.centre-mersenne.org/articles/10.1142/S1793744211000412/
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