Turbulence simulations: scalable methods and data analytics

Abstract:  Recent advances in computing technology have made numerical simulations an indispensable research tool in understanding fluid flow phenomena in complex conditions at great detail. Due to the nonlinear nature of the governing Navier-Stokes equations, simulations of high Reynolds number turbulent flows are computationally very expensive and demand for extreme levels of parallelism. In the first part of this talk, we present a brief overview of the current state-of-the-art turbulent flow simulations and present the issue that are likely to effect the scalability of simulations on future exascale computing systems. We investigate a novel approach based on widely used finite-difference schemes in which computations are carried out in an asynchronous fashion, i.e. synchronization of data among processing elements is not enforced and computations proceed regardless of the status of communication. This drastically reduces the CPU idle time and results in much larger computation rates and scalability. We show that while these schemes remain stable, their accuracy is significantly effected. We present new asynchrony-tolerant schemes that can maintain the accuracy under relaxed synchronization conditions. Performance of these schemes will be illustrated using simulations of simple models like Burgers’ equation.

In the second part of the talk, we propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. We apply the algorithm to a turbulent auto-ignition combustion case and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps.