Towards large-scale three-dimensional blood flow simulations in realistic geometries

Céline Caldini Queiros (1, 2) , Vincent Chabannes (3, 4) , Mourad Ismail (5) , Gonçalo Pena (6) , Christophe Prud'Homme (7) , Marcela Szopos (7) , Ranine Tarabay (7)

1 CALVI - Scientific computation and visualization
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 DYFCOM - DYnamique des Fluides COmplexes et Morphogénèse [Grenoble]
4 EDP - Equations aux Dérivées Partielles
5 LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
6 CMUC - Center for Mathematics [Coimbra]
7 IRMA - Institut de Recherche Mathématique Avancée

This paper addresses the numerical approximation of fluid dynamics problems using various finite element methods including high order methods and high order geometry. The paper is divided in three parts. The first part concerns the various problem formulations and discretization methods we are interested in. Using the Stokes equations as model, several different types of boundary conditions are presented and discussed. The second part deals with describing the high performance framework \Feel with which we obtained the various numerical results including scalability studies. Finally we display numerical results: we start with convergence properties of the various formulations and associated discretization choices including high order geometries and we finish with a Navier-Stokes simulation within the cerebral venous system.

Mots clés: Scalability; Complex geometries; Blood flows; High order methods; Stokes; Navier-Stokes

Domaines: Equations aux dérivées partielles [math.AP]

Céline Caldini Queiros, Vincent Chabannes, Mourad Ismail, Gonçalo Pena, Christophe Prud'Homme, et al.. Towards large-scale three-dimensional blood flow simulations in realistic geometries. ESAIM: Proceedings, 2013, 43, pp.195-212. ⟨10.1051/proc/201343013⟩. ⟨hal-00786556⟩