Unlike ordinary liquids, complex fluids such as blood exhibit strange behavior mainly dependent underlying structures that compose them. Simulation of blood flow remains a formidable challenge for theoretical and numerical modeling whose interest is to develop methods and simulation tools for the medical community. We propose in this work a contribution to this project will be mainly focused on numerical and computational aspects. We are particularly interested in the interaction between the blood and the vascular wall, which plays an important role in the large arteries as the aorta. We also invested in transport simulation of blood cells in the blood. For solving partial differential equations describing our hemodynamic models we chose to use numerical methods whose accuracy can be increased arbitrarily. For this purpose, the main ingredients that have been used are textit {(i)} the finite element method based on Galerkin approximations of arbitrary order in space and geometry, (i) the ALE method for taking into account the mobility of areas for movements of arbitrary order, (ii) the implicit and semi-implicit coupling for fluid-structure interaction. We also propose a new formulation of the method of boundary extended to model the transport of deformable particles immersed in a fluid. Our numerical simulations were based on the library Feel++ specializing on the EDP resolution. In addition to implementing physical models, we have developed various features are necessary for the implementation our methods: interpolation, Galerkin non-standard method, ALE method, framework for fluid-structure interaction. In addition, the size and geometry of the complexity of the models involved, the transition to parallel computing was essential in order to achieve our simulations. Thus, we have described the development was carried out in the library to allow deployment of our programs on parallel architectures.
