CDF solutions of diffusion equation with random inputs
Abstract
Physical subsurface phenomena regulated by diffusion mechanisms can be affected by parametric uncertainty. We analyze the impact of random inputs on a diffusion-reaction system modeled through a second order parabolic conservation law with random reaction parameters. We develop a deterministic equation for the cumulative distribution function (CDF), whose effective coefficients depend on the statistical properties of the random inputs. The CDF equation is subject to uniquely specified boundary conditions. The results obtained through the CDF method are compared to analytical solutions and Monte Carlo simulations for a few computational examples to verify the impact of the approximations.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2014
- Bibcode:
- 2014AGUFM.H44E..05B
- Keywords:
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- 1816 Estimation and forecasting;
- 1846 Model calibration;
- 1847 Modeling;
- 1869 Stochastic hydrology