The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress towards optimal engine designs requires accurate and computationally affordable flow simulations, as well as uncertainty quantification (UQ). While traditional UQ techniques can become prohibitive under expensive simulations and high-dimensional parameter spaces, polynomial chaos (PC) surrogate modeling is a useful tool for alleviating some of the computational burden. However, non-intrusive quadrature-based constructions of PC expansions relying on a single high-fidelity model can still be quite expensive. We thus introduce a two-stage numerical procedure for constructing PC surrogates while making use of multiple models of different fidelity. The first stage involves an initial dimension reduction through global sensitivity analysis using compressive sensing. The second stage utilizes adaptive sparse quadrature on a multifidelity expansion to compute PC surrogate coefficients in the reduced parameter space where quadrature methods can be more effective. The overall method is used to produce accurate surrogates and to propagate uncertainty induced by uncertain boundary conditions and turbulence model parameters, for performance quantities of interest from large eddy simulations of supersonic reactive flows inside a scramjet engine.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertainparameters involvedandthe high computational costofflow simulations. These difficulties are addressedin this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying themin the current studyto large-eddy simulations ofajet incrossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system's stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.
Griffiths, Natalie A.; Hanson, Paul J.; Ricciuto, Daniel M.; Jensen, Anna M.; Malhotra, Avni; Mcfarlane, Karis J.; Norby, Richard J.; Sargsyan, Khachik; Sebestyen, Stephen D.; Shi, Xiaoying; Walker, Anthony P.; Ward, Eric J.; Warren, Jeffrey M.; Weston, David J.
We are conducting a large-scale, long-term climate change response experiment in an ombrotrophic peat bog in Minnesota to evaluate the effects of warming and elevated CO2 on ecosystem processes using empirical and modeling approaches. To better frame future assessments of peatland responses to climate change, we characterized and compared spatial vs. temporal variation in measured C cycle processes and their environmental drivers. We also conducted a sensitivity analysis of a peatland C model to identify how variation in ecosystem parameters contributes to model prediction uncertainty. High spatial variability in C cycle processes resulted in the inability to determine if the bog was a C source or sink, as the 95% confidence interval ranged from a source of 50 g C m-2 yr-1 to a sink of 67 g C m-2 yr-1. Model sensitivity analysis also identified that spatial variation in tree and shrub photosynthesis, allocation characteristics, and maintenance respiration all contributed to large variations in the pretreatment estimates of net C balance. Variation in ecosystem processes can be more thoroughly characterized if more measurements are collected for parameters that are highly variable over space and time, and especially if those measurements encompass environmental gradients that may be driving the spatial and temporal variation (e.g., hummock vs. hollow microtopographies, and wet vs. dry years). Together, the coupled modeling and empirical approaches indicate that variability in C cycle processes and their drivers must be taken into account when interpreting the significance of experimental warming and elevated CO2 treatments.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.4 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.
A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.3 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sen- sitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.
