Multiphase flows are subject to various modeling and numerical approximations which induce uncertainty in the reliability of overall dynamics. A notorious difficulty is the modeling of interfaces between two different fluids with different material properties, or reactive shock-bubble interactions. Accounting also for the dependency on experimentally determined parameters, multiphase flow models involve a wealth of uncertainties from algorithmic, epistemic to structural uncertainty. Fluid-particle interactions, on the other hand, may alter the very essence of the flow equations, inducing chaos in both experiments and simulations, even for linear reversible flows. The onset of chaos poses the question of state uncertainty, which is representative also for nonlinear flows. The complexity of multi-phase models is exhibited also at the computational level, rendering the study of uncertainty cumbersome also from a numerical standpoint, which subsequently demands either efficient algebraic treatments or the development of reduced-order models. We seek to present various approaches to these issues, on both academic examples and at-scale engineering problems, evaluating traditional uncertainty quantification methods as well as incorporating novel strategies such as probabilistic programming and hierarchical reinforcement learning.
14:00
Uncertainty quantification of the loss of reversibility in Stokesian dynamics
Oana Marin | Argonne National Laboratory | United States
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Oana Marin | Argonne National Laboratory | United States
The linearity of flows at very low Reynolds number allows for analytical solutions for the dynamics of a single spherical particle, as well as for the periodic motion of an immersed prolate/oblate body, motion known as a Jeffrey orbit. For three or more immersed blunt bodies, however, not only do such analytical solutions not exist, but the flow itself---although linear---is no longer reversible and even becomes chaotic. Numerical and experimental studies have been previously performed to identify Lyapunov exponents for various configurations; however, the connection with uncertainty in initial conditions has not been fully established. By employing a nonintrusive uncertainty quantification approach and exploiting the linearity of the system, we show on several flow configurations correlations between the propagation of uncertainty in initial conditions and the dominant Lyapunov exponent. The linearity of the equations allows us to reduce numerical errors in the time integration to computer precision, by taking advantage of strategies such as exponential time integration and global error estimator subtraction. Thus, we obtain precise computations of both Lyapunov exponents and propagation of statistical quantities.
14:30
Intelligent Inference for Multiphase Flows
Nikolaus Adams | Technical University of Munich | Germany
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Ludger Paehler | Technical University of Munich | Germany
Nikolaus Adams | Technical University of Munich | Germany
Reactive shock-bubble interactions with their intricate dynamics are a prototypical example of compressible multiphase flows on which we can validate new approaches to inference at the core of uncertainty quantification routines. The planar shock hitting the bubble leads to complex wave-interface interactions whose fine-scale turbulent structure can be resolved only at Kolmogorov scale, hence necessitating expensive direct numerical simulations. In addition to aleatoric uncertainties, the complex configuration introduces epistemic uncertainties, which aggravate calibration to experimental data. For this reason, rigorous quantification of uncertainties for such applications is of paramount interest. Nonintrusive sampling-based approaches offer significant advantages over intrusive approaches for such applications. But the computational demands of highly resolved simulations require exploitation of the underlying structural hierarchies in a multifidelity Monte Carlo approach. We propose using the multifidelity paradigm together with recent advances in probabilistic programming and hierarchical reinforcement learning. We couple our simulators with the uncertainties expressed natively in the probabilistic abstraction layer.
We develop a novel implementation of the hierarchical proximal policy optimization algorithm coupled with metalearning and apply it for sample management, achieving a more optimal resource allocation than that afforded by current approaches in the literature.
15:00
Data assimilation in multi-physical flows for the design of aeronautical propulsion systems
Luca Magri | University of Cambridge | United Kingdom
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Luca Magri | University of Cambridge | United Kingdom
In this talk, we present an overview of recent developments in data assimilation for some multiphysical problems relevant to aeronautical propulsion. The assumptions we make in reduced-order modeling add three forms of uncertainties: (i) the equations may lack some terms (model uncertainty); (ii) the initial state of the simulation is not fully known (state uncertainty); and (iii) the parameters are not fully known (parameter uncertainty). These uncertainties propagate in a multiphysical system as a result of nonlinear interactions among its parts. Therefore, although a good reduced-order model may be qualitatively correct, the uncertainties often make the predictions quantitatively incorrect. The challenge is to make qualitative models quantitatively accurate and, technically, to learn the model of a multiphysical system from the prior knowledge of its parts.
This talk discusses Bayesian statistical learning and variational methods to create an adaptive reduced-order model for on-the-fly model, state, and parameter estimation whenever reference data is available from high-fidelity simulations and experiments. The model readjusts itself on the fly, but the predictions do not violate the physical constraints. The computational methods are applied to three multiphysical problems of increasing complexity: a nonlinear time-delayed thermoacoustic system, fluid interface capturing and tracking with level-set methods, and turbulent reacting flow.
15:30
Impact of surface tension uncertainty on an immiscible rising bubble
Marieme Ngom | Argonne National Laboratory | United States
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Marieme Ngom | Argonne National Laboratory | United States
Oana Marin | Argonne National Laboratory | United States
The modeling of fluid-fluid interactions poses difficult numerical issues, both in terms of accurate treatment of interfacial jumps as well as the reliance on experimental measurements of the surface tension coefficient. To address this issue we study the impact of variations in surface tension measurements on various quantities of interest, such as mean curvature or pressure difference. We consider the case of a rising bubble modeled using a boundary integral formulation, since, unlike immersed boundary approaches in volumetric methods, the boundary integral framework provides an accurate model of the interface between two fluids. Containing the discontinuity in material properties that occurs at the interface of immiscible fluids to the model instead of allowing it to permeate the numerical discretization, isolates the uncertainties induced by the surface tension coefficient. Furthermore the boundary integral model is suitable for efficient algebraic computations using a block GMRES strategy and recycling of Krylov spaces, for both intrusive and nonintrusive UQ approaches.