A l'échelle macroscopique, la mécanique des milieux continus (MMC) rencontre parfois des difficultés à représenter correctement le comportement d'un système physique, du fait d'une modélisation insuffisante des phénomènes. Ces faiblesses sont particulièrement marquées dans les systèmes où les interfaces, qui font apparaître des échelles d'espace très différentes, jouent un rôle prépondérant : microfluidique, écoulements polyphasiques etc.. Or, dans de nombreux domaines, et notamment dans le milieu pétrolier, les modèles macroscopiques existants semblent insuffisants pour pouvoir traiter correctement les cas proposés. Par ailleurs, la méconnaissance des paramètres d’entrée d'une simulation macroscopique tels que les propriétés de transport, introduit parfois une mauvaise représentation de l’ensemble des processus diffusifs. La simulation à l'échelle microscopique, en l'occurrence la dynamique moléculaire classique (DM), peut pallier certains problèmes rencontrés par les approches macroscopiques, en permettant de mieux appréhender les divers processus physiques, notamment aux interfaces. Elle permet également de suppléer l’expérimentation, en permettant de calculer pour un fluide modèle les propriétés physiques du mélange étudié. Ainsi, à partir des ces données générées, il est possible de construire des corrélations palliant aux différents manques. Néanmoins, de par son caractère microscopique, cette approche ne permet de simuler que des échelles sub-micrométriques qui sont bien éloignées de la taille indispensable à la plupart des cas réalistes, qu’ils soient académiques ou industriels. En couplant les deux démarches, macroscopique et microscopique, de manière directe ou indirecte, il est donc envisageable d’accéder à des informations que l’une ou l’autre des ces approches ne peut fournir seule. / Hybrid atomistic-continuum methods allow the simulation of complex flows, depending on the intimate connection of many spatiotemporal scales : from the nanoscale to the microscale and beyond. By limiting the molecular description within a small localized region, for example near fluid/fluid or fluid/solid interfaces (breakdown of the continuum), these methods are useful to study large systems for reasonable times. Besides, there is a wide variety of applications for such hybrid methods, ranging from the micro- or nano-scale devices, and other industrial processes such as wetting, droplet formation, and biomolecules near interfaces. In this work, we present one scheme for coupling the Navier-Stokes set of equations with Molecular Dynamics. Among the existing alternatives to couple these two approaches, we have chosen to implement a domain decomposition algorithm based on the alternating Schwarz method. In this method, the flow domain is decomposed into two overlapping regions : an atomistic region described by molecular dynamics and a continuum region described by a finite volume discretization of the incompressible Navier-Stokes equations. The fundamental assumption is that the atomistic and the continuum descriptions match in the overlapping region, where the exchange of information is performed. The information exchange, requires the imposition of velocity from one sub-domain in the form of boundary conditions (Dirichlet)/constraints on the solver of the other subdomain and vice versa. The spatial coupling as well as the temporal coupling of the two approaches has been investigated in this work. To show the feasibility of such a coupling, we have applied the multiscale method to a classical fluid mechanics problems.

Abstract Spontaneous changes in protein systems, such as the binding of a ligand to an enzyme or receptor, are characterized by a decrease of free energy. Despite the recent developments in computing power and methodology, it remains challenging to accurately estimate free energy changes. Major issues are still concerned with the accuracy of the underlying model to describe the protein system and how well the calculation in fact emulates the behaviour of the system. This thesis is largely concerned with the quality of current free energy calculation methods as applied to protein-ligand systems. Several methodologies were employed to calculate Gibbs standard free energies of binding for a collection of protein-ligand complexes, for which experimental affinities were available. Calculations were performed using system description with different levels of accuracy and included a continuum approach, which considers the protein and the ligand at the atomic level but includes solvent as a polarizable continuum, and an all-atom approach that relies on molecular dynamics simulations. In most such applications, the effects of ionic strength are neglected. However, the severity of this approximation, in particular when calculating free energies of charged ligands, is not very clear. The issue of incorporating ionic strength in free energy calculations by means of explicit ions was investigated in greater detail and considerable attention was given to the affinities of charged peptides in the presence of explicit counter-ions. A second common approximation is concerned with the description of ligands that exhibit multiple protonation states. Because most of current methods do not model changes in the acid dissociation constants of titrating groups upon binding, protonation equilibria of such ligands are not taken into account in free energy calculations. The implications of this approximation when predicting affinities were analysed. Finally, when calculating free energies of binding, a correct description of the interactions between the protein and the ligand is of fundamental importance. However, active sites of enzymes, where strained conformations may hold a functional role, are not always accurately modelled by molecular mechanics force fields. The case of a strained planar proline in the active site of triosephosphate isomerase was investigated using an hybrid quantum mechanics/molecular mechanics method, which implies a higher level of accuracy.