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

• Published in: ESAIM. Proceedings Vol. 43; pp. 195 - 212
• Main Authors: Caldini-Queiros, Céline, Chabannes, Vincent, Ismail, Mourad, Pena, Goncalo, Prud’homme, Christophe, Szopos, Marcela, Tarabay, Ranine
• Format: Journal Article
• Language: English
• Published: EDP Sciences 01.12.2013
• Subjects: Analysis of PDEs; Approximation; Computational fluid dynamics; Computer simulation; Convergence; Discretization; Mathematical analysis; Mathematical models; Mathematics; Navier-Stokes equations; Navier-Stokes; Stokes; Scalability; High order methods; Complex geometries; Blood flows
• ISSN: 1270-900X; 1270-900X
• DOI: 10.1051/proc/201343013

This paper addresses the numerical approximation of uid 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.