Search

In short-range molecular dynamics (MD) simulations, inhomogeneous particle distributions that dynamically change over time require flexible load-balancing methods to achieve good parallel efficiency. We have realized a general framework that can support different load-balancing methods and that can extend existing simulation packages in a minimally invasive way. This is a follow-up to recent work where we integrated it into the MD software ESPResSo to support load-balancing. We have realized a first partitioning strategy based on space-filling curves that can be used for efficient load-balanced multi-physics simulations. In this work we present a new graph-based partitioning strategy that leads to unstructured spatial domain decompositions and integrates well into the existing framework. We apply this to an inhomogeneous soot agglomeration scenario. For several load metrics, graph partitioning leads to better results than space-filling curves. The results indicate that the parallel performance for a given scenario requires a delicate combination of partitioning strategy and load metrics.

In this paper we present a coarse-graining (CG) approach for the agglomeration of nano-particles and clusters. In the current context, coarse-graining involves the replacement of fractal-like clusters by "representative" spherical particles. This simplification reduces significantly the number of degrees of freedom and allows for the computation of much larger systems and for better collision statistics of larger clusters. However, detailed information on the cluster shape is lost, but it is exactly this detailed shape that determines collision frequencies between fractal clusters and thus the agglomerates' growth. Therefore, additional properties need to be "inherited" by the coarsegrained particle that ensure similar collision frequencies. We generate collision probabilities as functions of the minimum passing distance between the clusters and provide these as additional function to the CG particle. This allows for partial overlap between CG particles, and the collision/sticking event is triggered with a specific probability only. We compare collision frequencies of CG simulations with equivalent Langevin dynamics simulations where all primary particles are tracked, and we observe decent agreement between cluster growth predicted by CG and the detailed Langevin dynamics simulations. Remaining differences may stem from differences in cluster transport.

A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of parameters in constitutive relations, and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitrary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation, and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally, we offer suggestions about the methods’ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.

The present paper uses Langevin dynamics (LD) to investigate the aggregation of soot nano-particles in turbulent flows. Interparticle forces are included, and the computation of the individual particles by LD is retained even after aggregate formation such that collision events and locations can be based on center-to-center particle distances without invoking any modelling assumptions of aggregate shape and/or collision frequency. We focus on the interactions between the specific hydrodynamic conditions and the particle properties and their effect on the resulting agglomerates’ morphologies. The morphology is characterized by the fractal dimension, D f . Computations of particle aggregation in homogeneous isotropic turbulence and in shear flows dominated by counter-rotating vortices with a wide range of turbulence intensities and particle sizes indicate that the evolution of the agglomerates’ shapes can be adequately parameterized by the size of the agglomerates and the Knudsen and Peclet numbers, the latter being based on the smallest turbulence scales. The computations further suggest that the shapes of agglomerates of certain sizes are relatively independent of time and relatively insensitive to larger turbulence structures. The fractal dimensions are modelled as functions of radius of gyration, Kn and Pe. The fitted expressions show good agreement with the LD simulations and represent the entire growth process of the agglomerates. A direct comparison of selected aggregates with experimental data shows very good qualitative agreement. A thorough quantitative validation of the evolution of the computed aggregate characteristics is, however, presently hindered by the challenges for and therefore lack of suitable experiments under appropriately controlled conditions.

The original publication has been updated. In the original publication of this article, under the Introduction heading section, the corrections to the second paragraph’s inline equation were not incorporated. The author’s additional corrections have also been incorporated. The publisher apologizes for the error made during production.

This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the so-called EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young’s modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio $${\delta }/{\varDelta X}=3$$ for a wide range of materials, if an error of 5 % is acceptable.

Gaining knowledge out of vast datasets is a main challenge in data-driven applications nowadays. Sparse grids provide a numerical method for both classification and regression in data mining which scales only linearly in the number of data points and is thus well-suited for huge amounts of data. Due to the recursive nature of sparse grid algorithms and their classical random memory access pattern, they impose a challenge for the parallelization on modern hardware architectures such as accelerators. In this paper, we present the parallelization on several current task- and data-parallel platforms, covering multi-core CPUs with vector units, GPUs, and hybrid systems. We demonstrate that a less efficient implementation from an algorithmical point of view can be beneficial if it allows vectorization and a higher degree of parallelism instead. Furthermore, we analyze the suitability of parallel programming languages for the implementation. Considering hardware, we restrict ourselves to the x86 platform with SSE and AVX vector extensions and to NVIDIA’s Fermi architecture for GPUs. We consider both multi-core CPU and GPU architectures independently, as well as hybrid systems with up to 12 cores and 2 Fermi GPUs. With respect to parallel programming, we examine both the open standard OpenCL and Intel Array Building Blocks, a recently introduced high-level programming approach, and comment on their ease of use. As the baseline, we use the best results obtained with classically parallelized sparse grid algorithms and their OpenMP-parallelized intrinsics counterpart (SSE and AVX instructions), reporting both single and double precision measurements. The huge data sets we use are a real-life dataset stemming from astrophysics and artificial ones, all of which exhibit challenging properties. In all settings, we achieve excellent results, obtaining speedups of up to 188 × using single precision on a hybrid system.