THESE présenté pour obtenir LE TITRE DE DOCTEUR DE L'INSTITUT NATIONAL POLYTECHNIQUE DE TOULOUSE
Spécialité : Génie des Procédés et de l'Environnement
par Young-il LIM
Méthodes de maillage adaptatif pour la résolution des équations différentielles partielles : Application à la simulation des systèmes dynamiques
ABSTRACT This work deals with the numerical solution of Partial Differential Equations (PDEs) in the presence of moving fronts along one or two spatial directions. Especially, we focus on spatial discretization methods on fixed or moving meshes for the convection-dominated systems in chemical engineering problems. In part I, fourteen discretization schemes on flexible stencils (fixed/adaptive/weighted stencils) within the fixed grid structure are compared in terms of stability, accuracy and temporal performance before using them within the moving mesh structure. The four of the 14 flexible stencil schemes tested are selected as the best methods compromised with the three criteria such as stability, accuracy and calculation time, using the multi-objective optimization concept. The WENO (Weighted Essentially-Non Oscillatory) scheme is particularly shown to be promising, since it dose not produce a spurious oscillation even near shocks and its numerical solution is accurate within a reasonable calculation time.
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