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At least 19 records

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-fly during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. The filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characterizing NWP Model Errors Using Doppler-Lidar Measurements of Recurrent Regional Diurnal Flows: Marine-Air Intrusions into the Columbia-River Basin

Ground-based Doppler-lidar instrumentation provides atmospheric wind data at dramatically improved accuracies and spatial/temporal resolutions. These capabilities have provided new insights into atmospheric flow phenomena, but they also should have a strong role in NWP model improvement. Insight into the nature of model errors can be gained by studying recurrent atmospheric flows, here a regional summertime diurnal sea breeze and subsequent marine-air intrusion into the arid interior of Oregon-Washington, where these winds are an important windenergy resource. These marine intrusions were sampled by three scanning Doppler lidars in the Columbia-River Basin as part of the Second Wind Forecast Improvement Project (WFIP2), using data from summer 2016. Lidar time-height cross sections of wind speed identified eight days when the diurnal-flow cycle, (peak wind speeds at midnight, afternoon minima) was obvious and strong. Eight-day composite time-height cross sections of lidar wind speeds are used to validate those generated by the operational NCEP-HRRR model. HRRR simulated the diurnal wind cycle, but produced errors in the timing of onset and significant errors due to a premature nighttime demise of the intrusion flow, producing low-bias errors of 6 m s-1 . Day-to-day and in the composite, whenever a marine intrusion occurred, HRRR made these same errors. The errors occurred under a range of gradient wind conditions indicating that they resulted from the misrepresentation of physical processes within a limited region around the measurement locations. Because of their generation within a limited geographical area, field-measurement programs can be designed to find and address the sources of these NWP errors.

Banta, Robert M.↗

Four-dimensional electrical conductivity monitoring of stage-driven river water intrusion: Accounting for water table effects using a transient mesh boundary and conditional inversion constraints

Our paper describes and demonstrates two methods of providing a priori information to the surface-based time-lapse three-dimensional electrical resistivity tomography (ERT) problem for monitoring stage-driven or tide-driven surface water intrusion into aquifers. First, a mesh boundary is implemented that conforms to the known location of the water table through time, thereby enabling the inversion to place a sharp bulk conductivity contrast at that boundary without penalty. Moreover, a nonlinear inequality constraint is used to allow only positive or negative transient changes in EC to occur within the saturated zone, dependent on the relative contrast in fluid electrical conductivity between surface water and groundwater. A 3-D field experiment demonstrates that time-lapse imaging results using traditional smoothness constraints are unable to delineate river water intrusion. The water table and inequality constraints provide the inversion with the additional information necessary to resolve the spatial extent of river water intrusion through time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Flow Visualization of Intrusive and Non-Intrusive Configurations for Lunar- and Martian-Relevant Plume-Surface Interaction

Flow visualization of a heated, inert-gas plume impinging onto a rigid surface was performed in lunar- and Martian-relevant pressure conditions. The experimental campaign was part of a broader effort to improve predictive models and capabilities for plume-surface interactions in spacecraft landing environments relevant to the Moon and Mars. The experiments used the planar laser induced fluorescence (PLIF) technique to visualize the flow of the jet over both a full-plane configuration using a flat impingement plate and a half-plane configuration where the jet flow was bisected by a splitter edge mounted to the impingement plate. The latter configuration has been previously used to study erosion mechanisms in plume-surface interactions because the technique enables cross-sectional optical access for visualizing the plume-induced crater. However, this approach has some uncertainty regarding the influence of the splitter edge on the flow field. The present work evaluates the differences in flow structures and characteristics between the flat plate and splitter plate experimental configurations at eight unique test conditions with and without the splitter edge where the vacuum chamber pressure, nozzle mass flow rate, and height of the nozzle were varied. Several features are identified which differ between the flat plate and splitter plate comparison cases, and these are summarized in this paper. The results presented provide insights to the differences between intrusive and non-intrusive experimental configurations for plume-surface interaction studies that can be used to further validate predictive models and inform future ground and flight test results.

PLIF↗

Flow Visualization of Intrusive and Non-Intrusive Configurations for Lunar- and Martian-Relevant Plume-Surface Interaction

Flow visualization of a heated, inert-gas plume impinging onto a rigid surface was performed in lunar- and Martian-relevant pressure conditions. The experimental campaign was part of a broader effort to improve predictive models and capabilities for plume-surface interactions in spacecraft landing environments relevant to the Moon and Mars. The experiments used the planar laser-induced fluorescence (PLIF) technique to visualize the flow of the jet over both a full-space configuration using a flat impingement plate and a half-space configuration where the jet flow was bisected by a splitter edge mounted to the impingement plate. The latter configuration has been previously used to study erosion mechanisms in plume-surface interactions because the technique enables cross-sectional optical access for visualizing the plume-induced crater. However, this approach has some uncertainty regarding the influence of the splitter edge on the flow field. The present work evaluates the differences in flow structures and characteristics between the flat plate and splitter plate experimental configurations at eight unique test conditions with and without the splitter edge where the vacuum chamber pressure, nozzle mass flow rate, and height of the nozzle were varied. Several features are identified which differ between the flat plate and splitter plate comparison cases, and these are summarized in this paper. The results presented provide insights to the differences between intrusive and non-intrusive experimental configurations for plume-surface interaction studies that can be used to further validate predictive models and inform future ground and flight test results.

PLIF↗

Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)

This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗