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Articles written by Reagan, M.T.

  1. Le Maitre, O.P., Reagan, M.T., Najm, H.N., Ghanem, R.G., and Knio, O.M.. "A stochastic projection method for fluid flow II.: random process" Journal of Computational Physics. 181 (1). 2002. pp. 9--44.

    An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.


  2. Le Maitre, O.P., Reagan, M.T., Debusschere, B.J., Najm, H.N., Ghanem, R.G., and Knio, O.M.. "Natural Convection in a Closed Cavity under Stochastic Non-Boussinesq Conditions" SIAM Journal on Scientific Computing. 26 (2). 2004. pp. 375--394.

    A stochastic projection method (SPM) is developed for quantitative propagation of uncertainty in compressible zero-Mach-number flows. The formulation is based on a spectral representation of uncertainty using the polynomial chaos (PC) system, and on a Galerkin approach to determining the PC coefficients. Governing equations for the stochastic modes are solved using a mass-conservative projection method. The formulation incorporates a specially tailored stochastic inverse procedure for exactly satisfying the mass-conservation divergence constraints. A brief validation of the zero-Mach-number solver is first performed, based on simulations of natural convection in a closed cavity. The SPM is then applied to analyze the steady-state behavior of the heat transfer and of the velocity and temperature fields under stochastic non-Boussinesq conditions.


  3. Reagan, M.T., Najm, H.N., Debusschere, B.J., Le Maitre, O.P., Knio, O.M., and Ghanem, R.G.. "Spectral stochastic uncertainty quantification in chemical systems" Combustion Theory and Modelling. 8 (3). SEP 2004. pp. 607--632.

    Uncertainty quantification (UQ) in the computational modelling of physical systems is important for scientific investigation, engineering design, and model validation. We have implemented an `intrusive' UQ technique in which (1) model parameters and field variables are modelled as stochastic quantities, and are represented using polynomial chaos (PC) expansions in terms of Hermite polynomial functions of Gaussian random variables, and (2) the deterministic model equations are reformulated using Galerkin projection into a set of equations for the time evolution of the field variable PC mode strengths. The mode strengths relate specific parametric uncertainties to their effects on model outputs. In this work, the intrusive reformulation is applied to homogeneous ignition using a detailed chemistry model through the development of a reformulated pseudospectral chemical source term. We present results analysing the growth of uncertainty during the ignition process. We also discuss numerical issues pertaining to the accurate representation of uncertainty with truncated PC expansions, and ensuing stability of the time integration of the chemical system.


  4. Reagan, M.T., Najm, H.N., Pebay, P.P., Knio, O.M., and Ghanem, R.G.. "Quantifying uncertainty in chemical systems modeling" International Journal of Chemical Kinetics. 37 (6). JUN 2005. pp. 368--382.

    This study compares two techniques for uncertainty quantification in chemistry computations, one based on sensitivity analysis and error propagation, and the other on stochastic analysis using polynomial chaos techniques. The two constructions are studied in the context of H-2-O-2 ignition under supercritical-water conditions. They are compared in terms of their prediction of uncertainty in species concentrations and the sensitivity of selected species concentrations to given parameters. The formulation is extended to one-dimensional reacting-flow simulations. The computations are used to study sensitivities to both reaction rate pre-exponentials and enthalpies, and to examine how this information must be evaluated in light of known, inherent parametric uncertainties in simulation parameters. The results indicate that polynomial chaos methods provide similar first-order information to conventional sensitivity analysis, while preserving higher-order information that is needed for accurate uncertainty quantification and for assigning confidence intervals on sensitivity coefficients. These higher-order effects can be significant, as the analysis reveals substantial uncertainties in the sensitivity coefficients themselves. © 2005 Wiley Periodicals, Inc.