CDF solutions of diffusion equation with random inputs

Francesca Boso, University of Calif San Diego, La Jolla, CA, United States and Daniel M Tartakovsky, Stanford University, Department of Energy Resources Engineering, Stanford, CA, United States
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.
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