Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems
Journal Article
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· Journal of Computational Physics
- Sandia National Laboratories, Livermore, CA 94551 (United States)
- Mechanical and Aerospace Engineering Dept., Sapienza University of Rome, Rome (Italy)
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.
- OSTI ID:
- 22314884
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 270; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
On the Statistical Calibration of Physical Models: STATISTICAL CALIBRATION OF PHYSICAL MODELS
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journal | February 2015 |
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