Notions clés des méthodes numériques dans le projet de NEPTUNE

We will try to present herein the main issues of our investigation in numerical methods for two-phase flow modeling, within the framework of the NEPTUNE project, which benefits from both contributions of CEA and EDF. These may be recast in five work packages. The first two are devoted to the mathematical and numerical modeling of two-phase flows with interfaces and the two-fluid two pressure approach. This in particular includes investigation of relaxation methods in order to establish correct links with standard two-fluid models, which are the core of the third work package. Computations of the interaction of shock waves with bubbles will be presented. Some new results concerning two-fluid and three-field flow modeling will also be briefly presented. Part of the work in the third work package concerns benchmarking, and comparison with several hyperbolic solvers, but also improvement of numerical treatment of source terms, multi-field models and suitable boundary conditions. The fourth one, which deals with the interfacial coupling of codes, is probably the most important one since it requires connecting all models together. Since little attention has been paid to this crucial point, part of the focus will be given in this paper on the coupling of equations of state, one-dimensional and three-dimensional codes, porous approach and free medium approach, but also on ongoing work concerning relaxed and unrelaxed hyperbolic two-phase flow models. The fifth work package gathers all classical contributions in numerical methods, including: recent applications of fictitious domain methods ; preconditioning of so-called “low Mach number” two-phase flows (with applications to the motion of rising bubbles in water) ; parallel and multigrid techniques (with applications to steam generators in nuclear power plants) ; Finite Volume Element methods (with applications to the standard two-fluid models) ; construction and validation of new exact or approximate Riemann solvers (in order to cope with vanishing phases). The latter five obviously aim at improving accuracy, stability and also at reducing CPU time. A few examples will enable to highlight the main advantages and possible drawbacks of these new developments, and the impact of the current and future increasing computational facilities. Main past achievements, and key points of current and future work on all these issues will be discussed. All available references will be given in order to help the reader getting a more accurate insight on these various contributions. The whole has clearly benefited from contributions of several PhD students : Thomas Fortin, Vincent Guillemaud, Olivier Hurisse, Angelo Muronne, Isabelle Ramiere, Jean-Michel Rovarch and Nicolas Seguin.