Cosmin Safta

A high-order low-Mach number AMR construction for chemically reacting flows

A high-order projection scheme was developed for the study of chemically reacting flows in the low-Mach number limit. The numerical approach for the momentum transport uses a combination of cell-centered/cell-averaged discretizations to achieve a fourth order formulation for the pressure projection algorithm. This scheme is coupled with a second order in time operator-split stiff approach for the species and energy equations. The code employs a fourth order, block-structured, adaptive mesh refinement approach to address the challenges posed by the large spectrum of spatial scales encountered in reacting flow computations. Results for advection-diffusion-reaction configurations are used to illustrate the performance of the numerical construction.

Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs

We outline a methodology for forward uncertainty quantification in systems with uncertain parameters, discontinuous model response, and a limited number of model runs. Our approach involves two stages. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve for arbitrarily distributed input parameters. Then, employing the Rosenblatt transform, we construct spectral representations of the uncertain model output, using polynomial chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged PC representation of the forward model response that allows efficient uncertainty quantification. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference. The uncertain model output is then computed by taking an ensemble average over PC expansions corresponding to sampled realizations of the discontinuity curve. The methodology is demonstrated on synthetic examples of discontinuous model response with adjustable sharpness and structure.

A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid

Abstract In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid–fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.

Fault Resilient Domain Decomposition Preconditioner for PDEs

The move towards extreme-scale computing platforms challenges scientific simulations in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of communication, system faults, and requirements of low-memory usage per core. In this work, we develop a novel framework for solving PDEs via domain decomposition that reformulates the solution as a state of knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication, and is generally well-suited for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demonstrate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit flips in the binary representation of subdomain solutions.

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.

Efficient Uncertainty Quantification in Stochastic Economic Dispatch

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on polynomial chaos expansions. These representations enable efficient and accurate propagation of uncertainties in model parameters, using sparse quadrature methods. We also use Karhunen–Loève expansions for efficient representation of uncertain renewable energy generation that follows geographical and temporal correlations derived from historical data at each wind farm. Considering expected production cost, we demonstrate that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.

Hybrid discrete/continuum algorithms for stochastic reaction networks

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis

In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis bacterium. In particular, the dependence of the competence state on rate constants of underlying reactions is investigated. We base our methodology on Polynomial Chaos (PC) spectral expansions that allow effective propagation of input parameter uncertainties to outputs of interest. Given a number of forward model training runs at sampled input parameter values, the PC modes are estimated using a Bayesian framework. As an outcome, these PC modes are described with posterior probability distributions. The resulting expansion can be regarded as an uncertain response function and can further be used as a computationally inexpensive surrogate instead of the original reaction model for subsequent analyses such as calibration or optimization studies. Furthermore, the methodology is enhanced with a classification-based mixture PC formulation that overcomes the difficulties associated with representing potentially nonsmooth input-output relationships. Finally, the global sensitivity analysis based on the multiparameter spectral representation of an observable of interest provides biological insight and reveals the most important reactions and their couplings for the competence dynamics.

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.

Structural models used in real-time biosurveillance outbreak detection and outbreak curve isolation from noisy background morbidity levels

OBJECTIVE We discuss the use of structural models for the analysis of biosurveillance related data. METHODS AND RESULTS Using a combination of real and simulated data, we have constructed a data set that represents a plausible time series resulting from surveillance of a large scale bioterrorist anthrax attack in Miami. We discuss the performance of anomaly detection with structural models for these data using receiver operating characteristic (ROC) and activity monitoring operating characteristic (AMOC) analysis. In addition, we show that these techniques provide a method for predicting the level of the outbreak valid for approximately 2 weeks, post-alarm. CONCLUSIONS Structural models provide an effective tool for the analysis of biosurveillance data, in particular for time series with noisy, non-stationary background and missing data.