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

¹ Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray 25030 Besançon Cedex, France
² Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble Cedex 9, France,
Tel.: +33476635497, Fax: +33476631263
³ Université Grenoble 1 / CNRS, Laboratoire Interdisciplinaire de Physique / UMR 5588. Grenoble, F-38041, France
⁴ CMUC, Department of Mathematics, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal
⁵ Université de Strasbourg / CNRS, IRMA / UMR 7501. Strasbourg, F-67000, France

Abstract

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.