Habib N. Najm

TChem - A Software Toolkit for the Analysis of Complex Kinetic Models

The TChem toolkit is a software library that enables numerica l simulations using complex chemistry and facilitates the analysis of detailed kinetic mode ls. The toolkit provide capabilities for thermodynamic properties based on NASA polynomials and species production/consumption rates. It incorporates methods that can selectively modify reaction parameters for sensitivity analysis. The library contains several functions that provide analytica lly computed Jacobian matrices necessary for the efficient time advancement and analysis of detailed k inetic models.

Uncertainty Quantification Methods for Model Calibration Validation and Risk Analysis.

The NASA Langley Multidisciplinary Uncertainty Quantification Challenge1 presents several questions, formulated around computer models that describe realistic aeronautical applications. These models are presented in a “blackbox” formulation to encourage discipline-independent approaches. The schematic in Fig. 1 illustrates the general structure of the model inputs, outputs, and quantities of interest.

Global Sensitivity Analysis and Quantification of Model Error for Large Eddy Simulation in Scramjet Design

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress towards optimal engine designs requires both accurate flow simulations as well as uncertainty quantification (UQ). However, performing UQ for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. We address these difficulties by combining UQ algorithms and numerical methods to the large eddy simulation of the HIFiRE scramjet configuration. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, helping reduce the stochastic dimension of the problem and discover sparse representations. Second, as models of different fidelity are available and inevitably used in the overall UQ assessment, a framework for quantifying and propagating the uncertainty due to model error is introduced. These methods are demonstrated on a non-reacting scramjet unit problem with parameter space up to 24 dimensions, using 2D and 3D geometries with static and dynamic treatments of the turbulence subgrid model.

Efficient uncertainty quantification methodologies for high-dimensional climate land models.

In this report, we proposed, examined and implemented approaches for performing efficient uncertainty quantification (UQ) in climate land models. Specifically, we applied Bayesian compressive sensing framework to a polynomial chaos spectral expansions, enhanced it with an iterative algorithm of basis reduction, and investigated the results on test models as well as on the community land model (CLM). Furthermore, we discussed construction of efficient quadrature rules for forward propagation of uncertainties from high-dimensional, constrained input space to output quantities of interest. The work lays grounds for efficient forward UQ for high-dimensional, strongly non-linear and computationally costly climate models. Moreover, to investigate parameter inference approaches, we have applied two variants of the Markov chain Monte Carlo (MCMC) method to a soil moisture dynamics submodel of the CLM. The evaluation of these algorithms gave us a good foundation for further building out the Bayesian calibration framework towards the goal of robust component-wise calibration.

A numerical scheme for modelling reacting flow with detailed chemistry and transport.

An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailedmorexa0» mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.«xa0less

Low Rank Approximation-based Quadrature for Fast Evaluation of Multi-Particle Integrals

Prashant Rai, Khachik Sargsyan , Habib Najm Sandia National Laboratories Support for this work was provided through the Scientific Discovery through Advanced Computing (SciDAC) project funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

An approach for estimating the uncertainty in ParaDiS predictions.

This report outlines an approach for computing the uncertainties in the predictions of computationally expensive models. While general, we use ParaDiS , a dislocation dynamics simulator originating in Lawrence Livermore National Laboratory, as the target application. ParaDiS is a mesoscale model, and uses submodels constructed/upscaled from microscale (molecular statics and dynamics) simulations. ParaDiS outputs, in turn, are upscaled and used in continuum (macroscale) simulations, e.g., those performed by ALE3D. This report addresses how one may quantify the uncertainties introduced by upscaling (both from microscale to mesoscale, and mesoscale to continuum), and the dependence of uncertainties in ParaDiS predictions on those of the inputs. This dependence is established via sensitivity analysis, and we address how this may be performed with a minimum of ParaDiS runs, given its immense computational cost. This includes constructing a smaller version of the model, sparse sampling of the parameter space, and exploiting the asymptotic nature of the time-evolution of the model outputs. The report concludes with a discussion of the computational resources required to perform this uncertainty quantification study.

Risk assessment of climate systems for national security.

Climate change, through drought, flooding, storms, heat waves, and melting Arctic ice, affects the production and flow of resource within and among geographical regions. The interactions among governments, populations, and sectors of the economy require integrated assessment based on risk, through uncertainty quantification (UQ). This project evaluated the capabilities with Sandia National Laboratories to perform such integrated analyses, as they relate to (inter)national security. The combining of the UQ results from climate models with hydrological and economic/infrastructure impact modeling appears to offer the best capability for national security risk assessments.

Uncertainty quantification for large-scale ocean circulation predictions.

Uncertainty quantificatio in climate models is challenged by the sparsity of the available climate data due to the high computational cost of the model runs. Another feature that prevents classical uncertainty analyses from being easily applicable is the bifurcative behavior in the climate data with respect to certain parameters. A typical example is the Meridional Overturning Circulation in the Atlantic Ocean. The maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO{sub 2} forcing. We develop a methodology that performs uncertainty quantificatio in the presence of limited data that have discontinuous character. Our approach is two-fold. First we detect the discontinuity location with a Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve location in presence of arbitrarily distributed input parameter values. Furthermore, we developed a spectral approach that relies on Polynomial Chaos (PC) expansions on each sides of the discontinuity curve leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification and propagation. The methodology is tested on synthetic examples of discontinuous data with adjustable sharpness and structure.

Uncertainty quantification of cinematic imaging for development of predictive simulations of turbulent combustion.

Recent advances in high frame rate complementary metal-oxide-semiconductor (CMOS) cameras coupled with high repetition rate lasers have enabled laser-based imaging measurements of the temporal evolution of turbulent reacting flows. This measurement capability provides new opportunities for understanding the dynamics of turbulence-chemistry interactions, which is necessary for developing predictive simulations of turbulent combustion. However, quantitative imaging measurements using high frame rate CMOS cameras require careful characterization of the their noise, non-linear response, and variations in this response from pixel to pixel. We develop a noise model and calibration tools to mitigate these problems and to enable quantitative use of CMOS cameras. We have demonstrated proof of principle for image de-noising using both wavelet methods and Bayesian inference. The results offer new approaches for quantitative interpretation of imaging measurements from noisy data acquired with non-linear detectors. These approaches are potentially useful in many areas of scientific research that rely on quantitative imaging measurements.