Mixing Sinc kernels to improve interpolations in smoothed particle hydrodynamics without pairing instability

The smoothed particle hydrodynamics technique strongly relies on the proper choice of interpolating functions. In this work, we revisit and extend the main properties of a family of interpolators called $Sinc~kernels$ and compare them with those of the widely used family of Wendland kernels. We show that a linear combination of low and high-order Sinc kernels generates good quality interpolators, which are resistant to the pairing instability while keeping good sampling properties in a wide range of neighbor interpolating points, $60\le n_b\le 400$. We show that a particular case of this linear mix of Sincs produces a well-balanced and robust kernel, that improves previous results in the Gresho-Chan vortex experiment even when the number of neighbors is not large, while yielding a good convergence rate. Although such a mixing technique is ideally suited for Sinc kernels owing to their excellent flexibility, it can be easily applied to other interpolating families such as the B-splines and Wendland kernels.Comment: 13 pages, 14 figures, 4 tables, submitted to MNRA

Integral smoothed particle hydrodynamics with an improved partition of unit and a better track of contact discontinuities

The correct evaluation of gradients is at the cornerstone of the smoothed particle hydrodynamics (SPH) technique. Using an integral approach to estimate gradients has proven to enhance accuracy substantially. Such approach retains the Lagrangian structure of SPH equations and is fully conservative. In this paper we study, among other things, the connection between the choice of the volume elements (VEs), which enters in the SPH summations, and the accuracy in the gradient estimation within the integral approach scheme (ISPH). A new kind of VEs are proposed which improve the partition of unit and are fully compatible with the Lagrangian formulation of SPH, including the grad-h corrections. Using analytic considerations, simple static toy models in 1D, and a few full 3D test cases, we show that any improvement in the partition of unit also leads to a better calculation of gradients when the integral approach is used jointly. Additionally, we propose a simple-to-implement variant of the ISPH scheme which is more adequate to handle sharp density contrasts.Comment: 29 pages, 17 figures, submitted to Journal of Computational Physic

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

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. In this work, we propose and check a scheme to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called Sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the Sinc function). The scheme is checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities and the collapse of a sun-like polytrope. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalizing accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.Comment: 29 pages, 18 figures, accepted by A&

SPH-EXA: Enhancing the Scalability of SPH codes Via an Exascale-Ready SPH Mini-App

Numerical simulations of fluids in astrophysics and computational fluid dynamics (CFD) are among the most computationally-demanding calculations, in terms of sustained floating-point operations per second, or FLOP/s. It is expected that these numerical simulations will significantly benefit from the future Exascale computing infrastructures, that will perform 10^18 FLOP/s. The performance of the SPH codes is, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. In this work an extensive study of three SPH implementations SPHYNX, ChaNGa, and XXX is performed, to gain insights and to expose any limitations and characteristics of the codes. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH mini-app. We implemented a rotating square patch as a joint test simulation for the three SPH codes and analyzed their performance on a modern HPC system, Piz Daint. The performance profiling and scalability analysis conducted on the three parent codes allowed to expose their performance issues, such as load imbalance, both in MPI and OpenMP. Two-level load balancing has been successfully applied to SPHYNX to overcome its load imbalance. The performance analysis shapes and drives the design of the SPH-EXA mini-app towards the use of efficient parallelization methods, fault-tolerance mechanisms, and load balancing approaches.Comment: arXiv admin note: substantial text overlap with arXiv:1809.0801

Self-gravitating barotropic equilibrium configurations of rotating bodies with SPH

We present a novel relaxation method to build three-dimensional rotating structures of barotropic bodies using the SPH technique. The method is able to relax gaseous structures in rigid as well as differential rotation. The relaxation procedure strongly relies on the excellent conservation of angular momentum that characterizes the SPH technique. The method has been successfully applied to a variety of zero-temperature white dwarfs and polytropic self-gravitating structures. Our SPH results have been validated by comparing the main features (energies, central densities and the polar to equatorial radius ratio) to those obtained with independent, albeit grid-based methods, as for example, the self-consistent field method, showing that both methods agree within few percents.Comment: 12 pages, 6 figures, 4 Tables, accepted for publication in Astronomy and Astrophysic

Detection of Silent Data Corruptions in Smoothed Particle Hydrodynamics Simulations

Silent data corruptions (SDCs) hinder the correctness of long-running scientific applications on large scale computing systems. Selective particle replication (SPR) is proposed herein as the first particle-based replication method for detecting SDCs in Smoothed particle hydrodynamics (SPH) simulations. SPH is a mesh-free Lagrangian method commonly used to perform hydrodynamical simulations in astrophysics and computational fluid dynamics. SPH performs interpolation of physical properties over neighboring discretization points (called SPH particles) that dynamically adapt their distribution to the mass density field of the fluid. When a fault (e.g., a bit-flip) strikes the computation or the data associated with a particle, the resulting error is silently propagated to all nearest neighbors through such interpolation steps. SPR replicates the computation and data of a few carefully selected SPH particles. SDCs are detected when the data of a particle differs, due to corruption, from its replicated counterpart. SPR is able to detect many DRAM SDCs as they propagate by ensuring that all particles have at least one neighbor that is replicated. The detection capabilities of SPR were assessed through a set of error-injection and detection experiments and the overhead of SPR was evaluated via a set of strong-scaling experiments conducted on a HPC system. The results show that SPR achieves detection rates of 91-99.9%, no false-positives, at an overhead of 1-10%

Axisymmetric magneto-hydrodynamics with SPH

Many interesting terrestrial and astrophysical scenarios involving magnetic fields can be approached in axial geometry. Even though the Lagrangian smoothed particle hydrodynamics (SPH) technique has been successfully extended to handle magneto-hydrodynamic (MHD) problems, a well-verified, axisymmetric MHD scheme based on the SPH technique does not exist. In this work, we propose and check a new axisymmetric MHD hydrodynamic code that can be applied to astrophysical and engineering problems which display an adequate geometry. We show that a hydrodynamic code built on these axisymmetric premises is able to produce similar results to standard 3D-SPHMHD codes but with much lesser computational effort.Comment: 9 pages, 6 figures. Proceedings of the 16th SPHERIC International Workshop (Catania, Italy 6-9 June 2022

A Smoothed Particle Hydrodynamics Mini-App for Exascale

The Smoothed Particles Hydrodynamics (SPH) is a particle-based, meshfree, Lagrangian method used to simulate multidimensional fluids with arbitrary geometries, most commonly employed in astrophysics, cosmology, and computational fluid-dynamics (CFD). It is expected that these computationally-demanding numerical simulations will significantly benefit from the up-and-coming Exascale computing infrastructures, that will perform 1018 FLOP/s. In this work, we review the status of a novel SPH-EXA mini-app, which is the result of an interdisciplinary co-design project between the fields of astrophysics, fluid dynamics and computer science, whose goal is to enable SPH simulations to run on Exascale systems. The SPH-EXA mini-app merges the main characteristics of three state-of-the-art parent SPH codes (namely ChaNGa, SPH-flow, SPHYNX) with state-of-the-art (parallel) programming, optimization, and parallelization methods. The proposed SPH-EXA mini-app is a C++14 lightweight and flexible header-only code with no external software dependencies. Parallelism is expressed via multiple programming models, which can be chosen at compilation time with or without accelerator support, for a hybrid process+thread+accelerator configuration. Strong- and weak-scaling experiments on a production supercomputer show that the SPH-EXA mini-app can be efficiently executed with up 267 million particles and up to 65 billion particles in total on 2,048 hybrid CPU-GPU nodes