Towards a Mini-App for Smoothed Particle Hydrodynamics at Exascale

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics represent computationally-demanding calculations. The parallelization of SPH codes is not trivial due to the absence of a structured grid. Additionally, the performance of the SPH codes can be, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. This work presents insights into the current performance and functionalities of three SPH codes: SPHYNX, ChaNGa, and SPH-flow. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH mini-app. To gain such insights, a rotating square patch test was implemented as a common test simulation for the three SPH codes and analyzed on two modern HPC systems. Furthermore, to stress the differences with the codes stemming from the astrophysics community (SPHYNX and ChaNGa), an additional test case, the Evrard collapse, has also been carried out. This work extrapolates the common basic SPH features in the three codes for the purpose of consolidating them into a pure-SPH, Exascale-ready, optimized, mini-app. Moreover, the outcome of this serves as direct feedback to the parent codes, to improve their performance and overall scalability.Comment: 18 pages, 4 figures, 5 tables, 2018 IEEE International Conference on Cluster Computing proceedings for WRAp1

Modelling High Speed Machining with the SPH Method

The purpose of this work is to evaluate the use of the Smoothed Particle Hydrodynamics (SPH) method within the framework of high speed cutting modelling. First, a 2D SPH based model is carried out using the LS-DYNA® software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control allows a “natural” workpiece/chip separation. The developed SPH model proves its ability to account for continuous and shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Then, The SPH model is used in order to improve the general understanding of machining with worn tools. At last, a milling model allowing the calculation of the 3D cutting forces is presented. The interest of the suggested approach is to be freed from classically needed machining tests: Those are replaced by 2D numerical tests using the SPH model. The developed approach proved its ability to model the 3D cutting forces in ball end milling

Derivation of SPH equations in a moving referential coordinate system

The conventional SPH method uses kernel interpolation to derive the spatial semi-discretisation of the governing equations. These equations, derived using a straight application of the kernel interpolation method, are not used in practice. Instead the equations, commonly used in SPH codes, are heuristically modified to enforce symmetry and local conservation properties. This paper revisits the process of deriving these semi-discrete SPH equations. It is shown that by using the assumption of a moving referential coordinate system and moving control volume, instead of the fixed referential coordinate system and fixed control volume used in the conventional SPH method, a set of new semi- discrete equations can be rigorously derived. The new forms of semi-discrete equations are similar to the SPH equations used in practice. It is shown through numerical examples that the new rigorously derived equations give similar results to those obtained using the conventional SPH equations

Kelvin-Helmholtz instabilities with Godunov SPH

Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka (2002). The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high density contrast, while the standard SPH shows the absence of the instability across a density gradient (Agertz et al. 2007). The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities. The blob test result coincides well with the results of the grid-based codes. An inaccurate handling of a density gradient in the standard SPH has been pointed out as the direct reason of the absence of the instabilities. An unphysical force happens at the density gradient even in a pressure equilibrium, and repulses particles from the initial density discontinuity. Therefore, the initial perturbation damps, and a gap forms at the discontinuity. The unphysical force has been studied in terms of the consistency of a numerical scheme. Contrary to the standard SPH, the momentum equation of the Godunov SPH doesnt use the particle approximation, and has been derived from the kernel convolution or a new Lagrangian function. The new Lagrangian function used in the Godunov SPH is more analogous to the real Lagrangian function for continuum. The momentum equation of the Godunov SPH has much better linear consistency, so the unphysical force is greatly reduced compared to the standard SPH in a high density contrast.Comment: 11 pages, 7 figures, Accepted for publication in MNRA