The study of hypersonic flows and their underlying aerothermochemical reactions is particularly important in the design and analysis of vehicles exiting and reentering Earth's atmosphere. Computational physics codes can be employed to simulate these phenomena; however, code verification of these codes is necessary to certify their credibility. To date, few approaches have been presented for verifying codes that simulate hypersonic flows, especially flows reacting in thermochemical nonequilibrium. In this work, we present our code-verification techniques for verifying the spatial accuracy and thermochemical source term in hypersonic reacting flows in thermochemical nonequilibrium. Additionally, we demonstrate the effectiveness of these techniques on the Sandia Parallel Aerodynamics and Reentry Code (SPARC).
Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle rules. In this paper, we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions. The first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules. The second approach better addresses large amounts of points, though it is less efficient than the first approach. We demonstrate the effectiveness of both approaches on singular integrands, which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules.
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.
Here, this work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Finally, numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.
The study of hypersonic flows and their underlying aerothermochemical reactions is particularly important in the design and analysis of vehicles exiting and reentering Earth’s atmosphere. Computational physics codes can be employed to simulate these phenomena; however, code verification of these codes is necessary to certify their credibility. To date, few approaches have been presented for verifying codes that simulate hypersonic flows, especially flows reacting in thermochemical nonequilibrium. In this paper, we present our code-verification techniques for hypersonic reacting flows in thermochemical nonequilibrium, as well as their deployment in the Sandia Parallel Aerodynamics and Reentry Code (SPARC).
This is the second of three related conference papers focused on verifying and validating a CFD model for laminar hypersonic flows. The first paper deals with the code verification and solution verification activities. In this paper, we investigate whether the model can accurately simulate laminar, hypersonic experiments of flows over double-cones, conducted in CUBRC’s LENS-I and LENS-XX wind-tunnels. The approach is to use uncertainty quantification and sensitivity analysis, along with a careful examination of experimental uncertainties, to perform validation assessments. The validation assessments use metrics that probabilistically incorporate both parametric (i.e. freestream input) uncertainty and experimental uncertainty. Further validation assessments compare these uncertainties to iterative and convergence uncertainties described in the first paper in our series of related papers. As other researchers have found, the LENS-XX simulations under-predict experimental heat flux measurements in the laminar, attached region of the fore-cone. This is observed for a deterministic simulation, as well as a probabilistic approach to creating an ensemble of simulations derived from CUBRC-provided estimates of uncertainty for freestream conditions. This paper will conclude with possible reasons that simulations cannot bracket experimental observations, and motivate the third paper in our series, which will further examine these possible explanations. The results in this study emphasize the importance of careful measurement of experimental conditions and uncertainty quantification of validation experiments. This study, along with its sister papers, also demonstrates a process of verification, uncertainty quantification, and quantitative validation activities for building and assessing credibility of computational simulations.
We propose a probabilistic framework for assessing the consistency of an experimental dataset, i.e., whether the stated experimental conditions are consistent with the measurements provided. In case the dataset is inconsistent, our framework allows one to hypothesize and test sources of inconsistencies. This is crucial in model validation efforts. The framework relies on statistical inference to estimate experimental settings deemed untrustworthy, from measurements deemed accurate. The quality of the inferred variables is gauged by its ability to reproduce held-out experimental measurements; if the new predictions are closer to measurements than before, the cause of the discrepancy is deemed to have been found. The framework brings together recent advances in the use of Bayesian inference and statistical emulators in fluid dynamics with similarity measures for random variables to construct the hypothesis testing approach. We test the framework on two double-cone experiments executed in the LENS-XX wind tunnel and one in the LENS-I tunnel; all three have encountered difficulties when used in model validation exercises. However, the cause behind the difficulties with the LENS-I experiment is known, and our inferential framework recovers it. We also detect an inconsistency with one of the LENS-XX experiments, and hypothesize three causes for it. We check two of the hypotheses using our framework, and we find evidence that rejects them. We end by proposing that uncertainty quantification methods be used more widely to understand experiments and characterize facilities, and we cite three different methods to do so, the third of which we present in this paper.
The study of hypersonic flows and their underlying aerothermochemical reactions is particularly important in the design and analysis of vehicles exiting and reentering Earth’s atmosphere. Computational physics codes can be employed to simulate these phenomena; however, code verification of these codes is necessary to certify their credibility. To date, few approaches have been presented for verifying codes that simulate hypersonic flows, especially flows reacting in thermochemical nonequilibrium. In this paper, we present our code-verification techniques for hypersonic reacting flows in thermochemical nonequilibrium, as well as their deployment in the Sandia Parallel Aerodynamics and Reentry Code (SPARC).
This project will enable high-fidelity aerothermal simulations of hypersonic vehicles to be employed (1) to generate large databases with quantified uncertainties and (2) for rapid interactive simulation. The databases will increase the volume/quality of A4H data; rapid interactive simulation can enable arbitrary conditions/designs to be simulated on demand. We will achieve this by applying reduced-order-modeling techniques to aerothermal simulations.
The SPARC (Sandia Parallel Aerodynamics and Reentry Code) will provide nuclear weapon qualification evidence for the random vibration and thermal environments created by re-entry of a warhead into the earth’s atmosphere. SPARC incorporates the innovative approaches of ATDM projects on several fronts including: effective harnessing of heterogeneous compute nodes using Kokkos, exascale-ready parallel scalability through asynchronous multi-tasking, uncertainty quantification through Sacado integration, implementation of state-of-the-art reentry physics and multiscale models, use of advanced verification and validation methods, and enabling of improved workflows for users. SPARC is being developed primarily for the Department of Energy nuclear weapon program, with additional development and use of the code is being supported by the Department of Defense for conventional weapons programs.
Computer Methods in Applied Mechanics and Engineering
Reddy, Sohail R.; Freno, Brian A.; Cizmas, Paul G.A.; Gokaltun, Seckin; Mcdaniel, Dwayne; Dulikravich, George S.
A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The Karush–Kuhn–Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user-defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. It was shown that the ROM and C-ROM produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.