Title :

Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation

Author(s) :

Mathis, Hélène [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Jacques-Louis Lions [LJLL]
Godlewski, Edwige [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Seguin, Nicolas [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Numerical Analysis, Geophysics and Ecology [ANGE]

Journal title :

Journal of Scientific Computing

Pages :

820-861

Publisher :

Springer Verlag

Publication date :

2015

ISSN :

0885-7474

English keyword(s) :

Chapman-Enskog expansion
dynamic model adaptation
relaxation
multiscale method
Hyperbolic system
finite volume methods
two-phase flows

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In numerous industrial CFD applications, it is usual to use two (or more)different codes to solve a physical phenomenon: where the flow is a priori assumed to have a simple behavior, a code based on a coarse model is ...
Show more >In numerous industrial CFD applications, it is usual to use two (or more)different codes to solve a physical phenomenon: where the flow is a priori assumed to have a simple behavior, a code based on a coarse model is applied, while a code based on a fine model is used elsewhere. This leads to a complex coupling problem with fixed interfaces. The aim of the present work is to provide a numerical indicator to optimize to position of these coupling interfaces. In other words, thanks to this numerical indicator, one could verify if the use of the coarser model and of the resulting coupling does not introduce spurious effects. In order to validate this indicator, we use it in a dynamical multiscale method with moving coupling interfaces. The principle of this method is to use as much as possible a coarse model instead of the fine model in the computational domain, in order to obtain an accuracy which is comparable with the one provided by the fine model. We focus here on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. Using a numerical Chapman-Enskog expansion and the distance to the equilibrium manifold, we construct the numerical indicator. Based on several works on the coupling of different hyperbolic models, an original numerical method of dynamic model adaptation is proposed. We prove that this multiscale method preserves invariant domains and that the entropy of the numerical solution decreases with respect to time. The reliability of the adaptation procedure is assessed on various 1D and 2D test cases coming from two-phase flow modeling.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL