ADAPTIVE TIME SPLITTING METHOD FOR MULTI-SCALE EVOLUTIONARY PARTIAL DIFFERENTIAL EQUATIONS

Confluentes Mathematici

DUMONT, THIERRY¹  LOUVET, VIOLAINE¹  MASSOT, MARC²  DESCOMBES, STÉPHANE²  DUARTE, MAX³ 

[1] Institut Camille Jordan - UMR CNRS 5208, Université de Lyon, Université Lyon 1, INSA de Lyon 69621, Ecole Centrale de Lyon, 43 Boulevard du 11 novembre 1918, Villeurbanne Cedex, 69622, France;Laboratoire EM2C - UPR CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, Chatenay-Malabry Cedex, 92295, France;Laboratoire J. A. Dieudonné - UMR CNRS 6621, Université Nice Sophia Antipolis, Parc Valrose, Nice Cedex 02, 06108, France

关键词: Time adaptive integration;    error control;    operator splitting;    reaction-diffusion;    multi-scale reaction waves;    multi-scale discharge;   

DOI  :  10.1142/S1793744211000412

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

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 disch...

【 授权许可】

Unknown