SUMMARYSince smoothed particle hydrodynamics (SPH) is based on interactions with the closer neighbouring particles, implementing the neighbour list is a key point in terms of the high performance of the code. The efficiency of the method depends directly on how to build and use the neighbour list. In the present work, the available searching algorithms for SPH codes are analyzed. Different gridding algorithms are evaluated, the gains in efficiency obtained from reordering of particles is investigated and the cell-linked list and Verlet list methods are studied to create the neighbour list. Furthermore, an innovative searching procedure based on a dynamic updating of the Verlet list is proposed. The efficiency of the algorithms is analyzed in terms of computational time and memory requirements.

An Arbitrary Lagrange Euler (ALE) description of fluid flows is used together with the meshless numerical method Smoothed Particle Hydrodynamics (SPH) to simulate free surface flows. The ALE description leads to an hybrid method that can be closely connected to the finite volume approach. It is then possible to adapt some common techniques like upwind schemes and preconditioning to remedy some of the well known drawbacks of SPH like stability and accuracy. An efficient boundary treatment based on a proper upwinding of fluid information at the boundary surface is settled. The resulting SPH-ALE numerical method is applied to simulate free surface flows encountered in Pelton turbines. RÉSUMÉ La méthode numérique sans maillage Smoothed Particle Hydrodynamics (SPH) est modifiée par l'adoption d'une description Arbitrary Lagrange Euler (ALE) des écoulements fluides, dans le but de simuler des écoulements à surface libre. Le formalisme ALE conduit à une méthode numérique hybride s'apparentant sur de nombreux points à une approche volumes finis. Il est alors possible d'adapter des techniques numériques courantes comme les schémas décentrés et le préconditionnement pour résoudre certains défauts majeurs de la méthode SPH, comme la stabilité numérique ou le manque de précision. Par ailleurs, le traitement des conditions limites est réalisé par un décentrement approprié des informations fluides sur les surfaces frontières. La méthode numérique SPH-ALE résultante est appliquée à la simulation d'écoulements à surface libre tels que ceux rencontrés dans les turbines Pelton.

This paper presents a brief review of grand challenges of Smoothed Particle Hydrodynamics (SPH) method. As a meshless method, SPH can simulate a large range of applications from astrophysics to free-surface flows, to complex mixing problems in industry and has had notable successes. As a young computational method, the SPH method still requires development to address important elements which prevent more widespread use. This effort has been led by members of the SPH rEsearch and engineeRing International Community (SPHERIC) who have identified SPH Grand Challenges. The SPHERIC SPH Grand Challenges (GCs) have been grouped into 5 categories: (GC1) convergence, consistency and stability, (GC2) boundary conditions, (GC3) adaptivity, (GC4) coupling to other models, and (GC5) applicability to industry. The SPH Grand Challenges have been formulated to focus the attention and activities of researchers, developers, and users around the world. The status of each SPH Grand Challenge is presented in this paper with a discussion on the areas for future development.

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Meshless methods are getting more and more popular in order to numerically simulate physical phenomena where an interface appears and plays an important role. Thanks to its fully Lagrangian formalism, the smoothed particle hydrodynamics method (SPH) is hence well suited to simulate free surface flows. The Pelton turbine is an hydraulic turbomachinery whose flow is challenging to simulate because of the complex rotating geometry, the free surface and the interaction between the runner and the casing. The work presented here aims at adapting SPH to simulate such a flow. The standard SPH model has first been successfully used to prove the capacity of the method in order to simulate flows in Pelton turbines. As the prediction of the pressure field on the bucket's surface is a key issue, a new simple model for the treatment of solid boundary conditions is proposed. Simulations of industrial test cases, including a complete rotating runner, are finally shown.volume of control, which is the Eulerian way to solve the equations of conservation, the Lagrangian formalism follows the fluid particles in their motion. A Lagrangian numerical method is hence a method in which calculation points are free to move together with the fluid motion. Some techniques [2] use a moving grid which has to be reconstructed when mesh distortion becomes penalizing, and are in fact a midway between Lagrangian and Eulerian methods. A much more convenient way and fully compliant with Lagrangian features is to avoid a grid to discretize the equations. It is then necessary to compute basic mathematical operators on a set of disordered points with the use of specific numerical schemes. These methods are called meshfree methods and among them, one of the most popular is the smoothed particle hydrodynamics (SPH) method. NUMERICAL MODELSPH was initially designed to simulate astrophysical phenomena like the formation and evolution of JPE465