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Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

Journal of Computational Physics

Najm, H.N.; Valorani, Mauro

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-fly during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. The filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits. © 2014.

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TYPE Journal Article YEAR 2014
ScopusOSTIDOI

Uncertainty quantification methods for model calibration validation, and risk analysis

16th AIAA Non-Deterministic Approaches Conference

Sargsyan, Khachik S.; Najm, H.N.; Chowdhary, Kamaljit S.; Debusschere, Bert D.; Swiler, Laura P.; Eldred, Michael S.

In this paper we propose a series of methodologies to address the problems in the NASA Langley Multidisciplinary UQ Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters in problem A, while variance-based global sensitivity analysis is proposed for problem B. For problems C and D we propose nested sampling methods for mixed aleatory-epistemic UQ.

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TYPE Conference YEAR 2014
DOIOSTIDOIScopusOSTIScopus

Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters

Combustion and Flame

Prager, Jens; Najm, H.N.; Sargsyan, Khachik S.; Safta, Cosmin S.

We study correlations among uncertain Arrhenius rate parameters in a chemical model for hydrocarbon fuel-air combustion. We consider correlations induced by the use of rate rules for modeling reaction rate constants, as well as those resulting from fitting rate expressions to empirical measurements arriving at a joint probability density for all Arrhenius parameters. We focus on homogeneous ignition in a fuel-air mixture at constant-pressure. We outline a general methodology for this analysis using polynomial chaos and Bayesian inference methods. We examine the uncertainties in both the Arrhenius parameters and in predicted ignition time, outlining the role of correlations, and considering both accuracy and computational efficiency. © 2013 The Combustion Institute.

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TYPE Journal Article YEAR 2013
OSTIScopus
Results 226–250 of 424
Results 226–250 of 424