Distributed Percolation Analysis for Turbulent Flows

Abstract

Percolation analysis is a valuable tool to study the statistical properties of turbulent flows. It is based on computing the percolation function for a derived scalar field, thereby quantifying the relative volume of the largest connected component in a superlevel set for a decreasing threshold. We propose a novel memory-distributed parallel algorithm to finely sample the percolation function. It is based on a parallel version of the union-find algorithm interleaved with a global synchronization step for each threshold sample. The efficiency of this algorithm stems from the fact that operations inbetween threshold samples can be freely reordered, are mostly local and thus require no inter-process communication. Our algorithm is significantly faster than previous algorithms for this purpose, and is neither constrained by memory size nor number of compute nodes compared to the conceptually related algorithm for extracting augmented merge trees. This makes percolation analysis much more accessible in a large range of scenarios. We explore the scaling of our algorithm for different data sizes, number of samples and number of MPI processes. We demonstrate the utility of percolation analysis using large turbulent flow data sets.

Notes on Percolation Analysis of Sampled Scalar Fields

“…The percolation function can be computed efficiently using an iterative Union-Find algorithm whose non-iterative version has first been suggested in the context of percolation by Hoshen and Kopelman [8]. The algorithm uses similar ingredients as a merge tree computation [4], has been adapted to work in a distributed setting for large-scale simulation data [7], and works as follows: We traverse all sample points x in decreasing order of their value f (x). We set p = f (x).…”

“…Alternative statistics such as the number of components are not as expressive, as they are rather featureless. For further exploration, see [7].…”

Towards replacing physical testing of granular materials with a Topology-based Model

“…A discontinuity in the resulting percolation function provides a threshold that describes an intrinsic porosity property of the material [27]. It has been adapted to finite domains and large material images [14].…”

Distributed merge forest

“…In atmospheric science, leaves and sub-trees of the merge tree are used to extract locally thresholded superlevel-set components around maxima to track high-pressure regions [21]. The volume of superlevel-set components is used to compute a percolation threshold, which is useful in studying a flow's turbulence and validating normalization schemes [7,10]. Although there exist several approaches to computing merge trees in a distributed setting [11,16,18], they are mainly focused on building a global data structure that is later used to answer topological queries.…”