Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows

Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical methods, scalable algorithms and re-design of current state-of-the art numerical solvers are required for scaling to these machines with minimal overheads. One such approach for partial differential equations based solvers involves computation of spatial derivatives with possibly delayed or asynchronous data using high-order asynchrony-tolerant (AT) schemes to facilitate mitigation of communication and synchronization bottlenecks without affecting the numerical accuracy. In the present study, an effective methodology of implementing temporal discretization using a multi-stage Runge-Kutta method with AT schemes is presented. Together these schemes are used to perform asynchronous simulations of canonical reacting flow problems, demonstrated in one-dimension including auto-ignition of a premixture, premixed flame propagation and non-premixed autoignition. Simulation results show that the AT schemes incur very small numerical errors in all key quantities of interest including stiff intermediate species despite delayed data at processing element (PE) boundaries. For simulations of supersonic flows, the degraded numerical accuracy of well-known shock-resolving WENO (weighted essentially non-oscillatory) schemes when used with relaxed synchronization is also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes are derived and tested on linear and non-linear equations. Finally the novel AT-WENO schemes are demonstrated in the propagation of a detonation wave with delays at PE boundaries

Towards Asynchronous Simulations of Turbulent Flows: Accuracy, Performance, and Optimization

Our understanding of turbulence has heavily relied on high-fidelity Direct Numerical Simulations (DNS) that resolve all dynamically relevant scales. But because of the inherent complexities of turbulent flows, these simulations are computationally very expensive and practically impossible at realistic conditions. Advancements in high performance computing provided much needed boost to the computational resources through increasing levels of parallelism and made DNS realizable, even though only in a limited parameter range. As the number of processing elements (PEs) in parallel machines increases, the penalties incurred in current algorithms due to necessary communications and synchronizations between PEs to update data become significant. These overheads are expected to pose a serious challenge to scalability on the next-generation exascale machines. An effective way to mitigate this bottleneck is through relaxation of strict communication and synchronization constraints and proceed with computations asynchronously i.e. without waiting for updated information from the other PEs. In this work, we investigate the viability of such asynchronous computing using high-order Asynchrony-Tolerant (AT) schemes for accurate and scalable simulations of reacting and non-reacting turbulence at extreme scales. For this, we first assess the important numerical properties of AT schemes, including conservation, stability, and spectral accuracy. Through rigorous mathematical analysis, we expose the breakdown of the standard von Neumann analysis for stability of multi-level schemes, even for widely used synchronous schemes. We overcome these limitations through what we call the generalized von Neumann analysis that is then used to assess stability of the AT schemes. Following which, we propose and implement two computational algorithms to introduce asynchrony in a three-dimensional compressible flow solver. We use these to perform first of a kind asynchronous simulation of compressible turbulence and analyze the effect of asynchrony on important physical characteristics of turbulence. Specifically we show that both large-scale and scale-scale features including highly intermittent instantaneous events, are accurately resolved by these algorithms. We also show excellent strong and weak scaling of asynchronous algorithms up to a processor count of P = 262144 because of significant reduction in communication overheads. As a precursor to the development of asynchronous combustion codes for simulations of more challenging problems with additional physical and numerical complexities, we investigate the effect of asynchrony on several canonical reacting flows. Furthermore, for problems with shocks and discontinuities, such as detonations, we derive and verify AT-WENO (weighted essentially non-oscillatory) schemes. With the ultimate goal to derive new optimal AT schemes we also develop a unified framework for the derivation of finite difference schemes. We show explicit trade-offs between order of accuracy, spectral accuracy and stability under this unifying framework, which can be exploited to devise very accurate numerical schemes for asynchronous computations on extreme scales with minimal overheads

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

The Inertial Range of Turbulence in the Inner Heliosheath and in the Local Interstellar Medium

The governing mechanisms of magnetic field annihilation in the outer heliosphere is an intriguing topic. It is currently believed that the turbulent fluctuations pervade the inner heliosheath (IHS) and the Local Interstellar Medium (LISM). Turbulence, magnetic reconnection, or their reciprocal link may be responsible for magnetic energy conversion in the IHS.   As 1-day averaged data are typically used, the present literature mainly concerns large-scale analysis and does not describe inertial-cascade dynamics of turbulence in the IHS. Moreover, lack of spectral analysis make IHS dynamics remain critically understudied. Our group showed that 48-s MAG data from the Voyager mission are appropriate for a power spectral analysis over a frequency range of five decades, from 5e-8 Hz to 1e-2 Hz [Gallana et al., JGR 121 (2016)]. Special spectral estimation techniques are used to deal with the large amount of missing data (70%). We provide the first clear evidence of an inertial-cascade range of turbulence (spectral index is between -2 and -1.5). A spectral break at about 1e-5 Hz is found to separate the inertial range from the enegy-injection range (1/f energy decay). Instrumental noise bounds our investigation to frequencies lower than 5e-4 Hz. By considering several consecutive periods after 2009 at both V1 and V2, we show that the extension and the spectral energy decay of these two regimes may be indicators of IHS regions governed by different physical processes. We describe fluctuations’ regimes in terms of spectral energy density, anisotropy, compressibility, and statistical analysis of intermittency.   In the LISM, it was theorized that pristine interstellar turbulence may coexist with waves from the IHS, however this is still a debated topic. We observe that the fluctuating magnetic energy cascades as a power law with spectral index in the range [-1.35, -1.65] in the whole range of frequencies unaffected by noise. No spectral break is observed, nor decaying turbulence

Numerical Simulations of Cavitating Bubbles in Elastic and Viscoelastic Materials for Biomedical Applications

The interactions of cavitating bubbles with elastic and viscoelastic materials play a central role in many biomedical applications. This thesis makes use of numerical modeling and data-driven approaches to characterize soft biomaterials at high strain rates via observation of bubble dynamics, and to model burst-wave lithotripsy, a focused ultrasound therapy to break kidney stones. In the first part of the thesis, a data assimilation framework is developed for cavitation rheometry, a technique that uses bubble dynamics to characterize soft, viscoelastic materials at high strain-rates. This framework aims to determine material properties that best fit observed cavitating bubble dynamics. We propose ensemble-based data assimilation methods to solve this inverse problem. This approach is validated with surrogate data generated by adding random noise to simulated bubble radius time histories, and we show that we can confidently and efficiently estimate parameters of interest within 5% given an iterative Kalman smoother approach and an ensemble- based 4D-Var hybrid technique. The developed framework is applied to experimental data in three distinct settings, with varying bubble nucleation methods, cavitation media, and using different material constitutive models. We demonstrate that the mechanical properties of gels used in each experiment can be estimated quickly and accurately despite experimental inconsistencies, model error, and noisy data. The framework is used to further our understanding of the underlying physics and identify limitations of our bubble dynamics model for violent bubble collapse. In the second part of the thesis, we simulate burst-wave lithotripsy (BWL), a non- invasive treatment for kidney stones that relies on repeated short bursts of focused ultrasound. Numerical approaches to study BWL require simulation of acoustic waves interacting with solid stones as well as bubble clouds which can nucleate ahead of the stone. We implement and validate a hypoelastic material model, which, with the addition of a continuum damage model and calibration of a spherically- focused transducer array, enables us to determine how effective various treatment strategies are with arbitrary stones. We present a preliminary investigation of the bubble dynamics occurring during treatment, and their impact on damage to the stone. Finally, we propose a strategy to reduce shielding by collapsing bubbles ahead of the stone via introduction of a secondary, low-frequency ultrasound pulse during treatment.</p

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Supersonic combustion modelling using the conditional moment closure approach

This work presents a novel algorithm for supersonic combustion modelling. The method involved coupling the Conditional Moment Closure (CMC) model to a fully compressible, shock capturing, high-order flow solver, with the intent of modelling a reacting hydrogen-air, supersonic jet. Firstly, a frozen chemistry case was analysed to validate the implementation of the algorithm and the ability for CMC to operate at its frozen limit. Accurate capturing of mixing is crucial as the mixing and combustion time scales for supersonic flows are on the order of milliseconds. The results of this simulation were promising even with an unexplainable excess velocity decay of the jet core. Hydrogen mass fractions however, showed fair agreement to the experiment. The method was then applied to the supersonic reacting case of ONERA. The results showed the method was able to successfully capture chemical non-equilibrium effects, as the lift-off height and autoignition time were reasonably captured. Distributions of reactive scalars were difficult to asses as experimental data was deemed to be very inaccurate. As a consequence, published numerical results for the same test case were utilised to aid in analysing the results of the presented simulations. Due to the primary focus of the study being to assess non-equilibrium effects, the clustering of the computational grid lent itself to smeared and lower magnitude wall pressure distributions. Nevertheless, the wall pressure distributions showed good qualitative agreement to experiment. The primary conclusions from the study were that the CMC method is feasible to model supersonic combustion. However, a more detailed analysis of sub-models and closure assumptions must be conducted to assess the feasibility on a more fundamental level. Also, from the results of both the frozen chemistry and the reacting case, the effects of assuming constant species Lewis number was visible