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Study on SPH Viscosity Term Formulations
For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified
Geometrically-exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods
We develop an Optimal Transportation Meshfree (OTM) particle method for
advection-diffusion in which the concentration or density of the diffusive
species is approximated by Dirac measures. We resort to an incremental
variational principle for purposes of time discretization of the diffusive
step. This principle characterizes the evolution of the density as a
competition between the Wasserstein distance between two consecutive densities
and entropy. Exploiting the structure of the Euler-Lagrange equations, we
approximate the density as a collection of Diracs. The interpolation of the
incremental transport map is effected through mesh-free max-ent interpolation.
Remarkably, the resulting update is geometrically exact with respect to
advection and volume. We present three-dimensional examples of application that
illustrate the scope and robustness of the method.Comment: 19 pages, 8 figure
SPH with the multiple boundary tangent method
In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent
treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid-driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved
solid boundaries, but the approach presented herein should be extendable to time-evolving, free-surface boundaries
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
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