arXiv subjects

Todd A. Oliver

Publications and source records attributed to Todd A. Oliver.

13 recordsLinked to original sources

arXiv2025

Quantifying Resolution Limits in Pedestal Profile Measurements with Gaussian Process Regression

Edge transport barriers (ETBs) in magnetically confined fusion plasmas, commonly known as pedestals, play a crucial role in achieving high confinement plasmas. However, their defining characteristic, a steep rise in plasma pressure over short length scales, makes them challenging to diagnose experimentally. In this work, we use Gaussian Process Regression (GPR) to develop first-principles metrics for quantifying the spatiotemporal resolution limits of inferring differentiable profiles of temperature, pressure, or other quantities from experimental measurements. Although we focus on pedestals, the methods are fully general and can be applied to any setting involving the inference of profiles from discrete measurements. First, we establish a correspondence between GPR and low-pass filtering, giving an explicit expression for the effective `cutoff frequency' associated with smoothing incurred by GPR. Second, we introduce a novel information-theoretic metric, $N_{eff}$, which measures the effective number of data points contributing to the inferred value of a profile or its derivative. These metrics enable a quantitative assessment of the trade-off between `over-fitting' and `over-regularization', providing both practitioners and consumers of GPR with a systematic way to evaluate the credibility of inferred profiles. We apply these tools to develop practical advice for using GPR in both time-independent and time-dependent settings, and demonstrate their usage on inferring pedestal profiles using measurements from the DIII-D tokamak.

physics.plasm-ph↗

arXiv2025

The Data Fusion Labeler (dFL): Challenges and Solutions to Data Harmonization, Labeling, and Provenance in Fusion Energy

Fusion energy research increasingly depends on the ability to integrate heterogeneous, multimodal datasets from high-resolution diagnostics, control systems, and multiscale simulations. The sheer volume and complexity of these datasets demand the development of new tools capable of systematically harmonizing and extracting knowledge across diverse modalities. The Data Fusion Labeler (dFL) is introduced as a unified workflow instrument that performs uncertainty-aware data harmonization, schema-compliant data fusion, and provenance-rich manual and automated labeling at scale. By embedding alignment, normalization, and labeling within a reproducible, operator-order-aware framework, dFL reduces time-to-analysis by greater than 50X (e.g., enabling >200 shots/hour to be consistently labeled rather than a handful per day), enhances label (and subsequently training) quality, and enables cross-device comparability. Case studies from DIII-D demonstrate its application to automated ELM detection and confinement regime classification, illustrating its potential as a core component of data-driven discovery, model validation, and real-time control in future burning plasma devices.

physics.plasm-ph↗

arXiv2024

Characterization of uncertainties in electron-argon collision cross sections

The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the key reaction rates and transport properties of the plasma. Although many cross sections have been identified through experiments and quantum mechanical simulations, their uncertainties are not well-investigated. We characterize the uncertainties in electron-argon collision cross sections using a Bayesian framework. Six collision processes -- elastic momentum transfer, ionization, and four excitations -- are characterized with semi-empirical models, whose parametric uncertainties effectively capture the features important to the macroscopic properties of the plasma, namely transport properties and chemical reaction rates. The method is designed to capture the effects of systematic errors that lead to large discrepancies between some data sets. Specifically, for the purposes of Bayesian inference, each of the parametric cross section models is augmented with a Gaussian process representing systematic measurement errors as well as model inadequacies in the parametric form. The results show that the method is able to capture scatter in the data between the electron-beam experiments and ab-initio quantum simulations. The calibrated cross section models are further validated against measurements from swarm-parameter experiments.

physics.plasm-ph↗

arXiv2023

Automated Estimation of Plasma Temperature and Density from Emission Spectroscopy

This paper introduces a novel approach for automated estimation of plasma temperature and density using emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is validated through experimental observations, focusing on individual and sequential shot analyses. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation, marking a significant advancement in the field of emission spectroscopy for plasma diagnostics. This study not only offers a new perspective in plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

physics.plasm-ph↗

arXiv2022

A pseudospectral method for direct numerical simulation of low-Mach, variable-density, turbulent flows

A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is employed in the two homogeneous spatial directions and a number of discretizations can be used in the inhomogeneous direction. The momentum is decomposed into divergence- and curl-free portions which allows the momentum equations to be rewritten, removing the need to solve for the pressure. The temporal discretization is based on an explicit, segregated Runge-Kutta method and the scalar equations are reformulated to directly address the redundancy of the equation of state and the mass conservation equation. An efficient, matrix-free, iterative solution of the resulting equations allows for second-order accuracy in time and numerical stability for large density ratios, which is demonstrated for ratios up to $\sim 25.7$.

physics.flu-dyn↗

arXiv2021

Active model split hybrid RANS/LES

Reliably predictive simulation of complex flows requires a level of model sophistication and robustness exceeding the capabilities of current Reynolds-averaged Navier-Stokes (RANS) models. The necessary capability can often be provided by well-resolved large eddy simulation (LES), but, for many flows of interest, such simulations are too computationally intensive to be performed routinely. In principle, hybrid RANS/LES (HRL) models capable of transitioning through arbitrary levels of modeled and resolved turbulence would ameliorate both RANS deficiencies and LES expense. However, these HRL approaches have led to a host of unique complications, in addition to those already present in RANS and LES. This work proposes a modeling approach aimed at overcoming such challenges. The approach presented here relies on splitting the turbulence model into three distinct components: two responsible for the standard subgrid model roles of either providing the unresolved stress or dissipation and a third which reduces the model length scale by creating resolved turbulence. This formulation renders blending functions unnecessary in HRL. Further, the split-model approach both reduces the physics-approximation burden on simple eddy-viscosity-based models and provides convenient flexibility in model selection. In regions where the resolution is adequate to support additional turbulence, fluctuations are generated at the smallest locally resolved scales of motion. This active forcing drives the system towards a balance between RANS and grid-resolved LES for any combination of resolution and flow while the split-model formulation prevents local disruption to the total stress. The model is demonstrated on fully-developed, incompressible channel flow [1] and the periodic hill [2], in which it is shown to produce accurate results and avoid common HRL shortcomings, such as model stress depletion.

physics.flu-dyn↗

arXiv2021

Numerical dispersion effects on the energy cascade in large-eddy simulation

Implicitly filtered large-eddy simulation (LES) is by nature numerically under-resolved. With the sole exception of Fourier-spectral methods, discrete numerical derivative operators cannot accurately represent the dynamics of all of the represented scales. Since the resolution scale in an LES usually lies in the inertial range, these poorly represented scales are dynamically significant and errors in their dynamics can affect all resolved scales. This Letter is focused on characterizing the effects of numerical dispersion error by studying the energy cascade in LES of convecting homogeneous isotropic turbulence. Numerical energy and transfer spectra reveal that energy is not transferred at the appropriate rate to wavemodes where significant dispersion error is present. This leads to a deficiency of energy in highly dispersive modes and an accompanying pile up of energy in the well resolved modes, since dissipation by the subgrid model is diminished. An asymptotic analysis indicates that dispersion error causes a phase decoherence between triad interacting wavemodes, leading to a reduction in the mean energy transfer rate for these scales. These findings are relevant to a wide range of LES, since turbulence commonly convects through the grid in practical simulations. Further, these results indicate that the resolved scales should be defined to not include the dispersive modes.

physics.flu-dyn↗

arXiv2021

Extensions to Multifidelity Monte Carlo Methods for Simulations of Chaotic Systems

Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for each level. For computationally intensive models, as are often encountered in simulations of chaotic systems, this up-front cost can be prohibitive. In this work, a correlation estimation procedure is developed for the case in which the highest and next highest fidelity models are generated via discretizing the same mathematical model using different resolution. The procedure uses discretization error estimates to estimate the required correlation coefficient without the need to sample the highest fidelity model, which can dramatically decrease the cost of the preprocessing phase. The method is extended to chaotic problems by using discretization error estimates that account for the statistical nature of common quantities of interest and the accompanying finite sampling errors that pollute estimates of such quantities of interest. The methodology is then demonstrated on a model problem based on the Kuramoto-Sivashinsky equation.

physics.data-an↗

arXiv2021

Effects of resolution inhomogeneity in large-eddy simulation

Large Eddy Simulation (LES) of turbulence in complex geometries is often conducted using strongly inhomogeneous resolution. The issues associated with resolution inhomogeneity are related to the noncommutativity of the filtering and differentiation operators, which introduces a commutation term into the governing equations. Neglect of this commutation term gives rise to commutation error. While the commutation error is well recognized, it is often ignored in practice. Moreover, the commutation error arising from the implicit part of the filter (i.e., projection onto the underlying discretization) has not been well investigated. Modeling the commutator between numerical projection and differentiation is crucial for correcting errors induced by resolution inhomogeneity in practical LES settings, which typically rely solely on implicit filtering. Here, we employ a multiscale asymptotic analysis to investigate the characteristics of the commutator. This provides a statistical description of the commutator, which can serve as a target for the statistical characteristics of a commutator model. Further, we investigate how commutation error manifests in simulation and demonstrate its impact on the convection of a packet of homogeneous isotropic turbulence through an inhomogeneous grid. A connection is made between the commutation error and the propagation properties of the underlying numerics. A modeling approach for the commutator is proposed that is applicable to LES with filters that include projections to the discrete solution space and that respects the numerical properties of the LES evolution equation. It may also be useful in addressing other LES modeling issues such as discretization error.

physics.flu-dyn↗

arXiv2018

Towards a Predictive Hybrid RANS/LES Framework

Predictive simulation of many complex flows requires moving beyond Reynolds-averaged Navier-Stokes (RANS) based models to representations resolving at least some scales of turbulence in at least some regions of the flow. To resolve turbulence where necessary while avoiding the cost of performing large eddy simulation (LES) everywhere, a broad range of hybrid RANS/LES methods have been developed. While successful in some situations, existing methods exhibit a number of deficiencies which limit their predictive capability in many cases of interest, for instance in many flows involving smooth wall separation. These deficiencies result from inappropriate blending approaches and resulting inconsistencies between the resolved and modeled turbulence as well as errors inherited from the underlying RANS and LES models. This work details these problems and their effects in hybrid simulations, and develops a modeling paradigm aimed at overcoming these challenges. The new approach discards typical blending approaches in favor of a hybridization strategy in which the RANS and LES model components act through separate models formulated using the mean and fluctuating velocity, respectively. Further, a forcing approach in which fluctuating content is actively transferred from the modeled to the resolved scales is introduced. Finally, the model makes use of an anisotropic LES model that is intended to represent the effects of grid anisotropy. The model is demonstrated on fully-developed, incompressible channel flow and shown to be very promising.

physics.flu-dyn↗

arXiv2017

A Temporal Slow Growth Formulation for Direct Numerical Simulation of Compressible Wall--Bounded Flows

A new slow growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow growth modeling concepts to complex boundary layer flows. As in previous slow growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the streamwise direction, which avoids the need for extremely long domains and complex inflow conditions that typically accompany spatially developing simulations. Further, it enables the use of efficient Fourier numerics. Unlike previous approaches, the present approach is based on a temporally evolving boundary layer and is specifically tailored to give results for calibration and validation of RANS turbulence models. The use of a temporal homogenization simplifies the modeling, enabling straightforward extension to flows with complicating features, including cold and blowing walls. To generate data useful for calibration and validation of RANS models, special care is taken to ensure that the mean slow growth forcing is closed in terms of the mean and other quantities that appear in standard RANS models, ensuring that there is no confounding between typical RANS closures and additional closures required for the slow growth problem. The performance of the method is demonstrated on two problems: an essentially incompressible, zero-pressure-gradient boundary layer and a transonic boundary layer over a cooled wall with wall transpiration.

physics.flu-dyn↗

arXiv2014

Validating Predictions of Unobserved Quantities

The ultimate purpose of most computational models is to make predictions, commonly in support of some decision-making process (e.g., for design or operation of some system). The quantities that need to be predicted (the quantities of interest or QoIs) are generally not experimentally observable before the prediction, since otherwise no prediction would be needed. Assessing the validity of such extrapolative predictions, which is critical to informed decision-making, is challenging. In classical approaches to validation, model outputs for observed quantities are compared to observations to determine if they are consistent. By itself, this consistency only ensures that the model can predict the observed quantities under the conditions of the observations. This limitation dramatically reduces the utility of the validation effort for decision making because it implies nothing about predictions of unobserved QoIs or for scenarios outside of the range of observations. However, there is no agreement in the scientific community today regarding best practices for validation of extrapolative predictions made using computational models. The purpose of this paper is to propose and explore a validation and predictive assessment process that supports extrapolative predictions for models with known sources of error. The process includes stochastic modeling, calibration, validation, and predictive assessment phases where representations of known sources of uncertainty and error are built, informed, and tested. The proposed methodology is applied to an illustrative extrapolation problem involving a misspecified nonlinear oscillator.

physics.data-an↗

arXiv2013

Estimating Uncertainties in Statistics Computed from DNS

Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier-Stokes equations. Due to the presence of non-trivial sampling error, standard techniques for estimating discretization error (such as Richardson extrapolation) fail or are unreliable. This work provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as part of a Bayesian extension of Richardson extrapolation in order to characterize the discretization error. These methods are tested using the Lorenz equations and are shown to perform well. These techniques are then used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow. For both cases, it is found that while the sampling uncertainty is large enough to make the order of accuracy difficult to determine, the estimated discretization errors are quite small. This indicates that the commonly used heuristics provide ad- equate resolution for this class of problems. However, it is also found that, for some quantities, the discretization error is not small relative to sampling error, indicating that the conventional wisdom that sampling error dominates discretization error for this class of simulations needs to be reevaluated.

physics.flu-dyn↗