Exact PDF equations and closure approximations for advective-reactive transport

Journal Article · Sat Jun 01 04:00:00 EDT 2013 · Journal of Computational Physics, 243:323-343

DOI:https://doi.org/10.1016/j.jcp.2013.03.001· OSTI ID:1177357

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.; Karniadakis, George E.

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recently proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1177357
• Report Number(s): PNNL-SA-97278; KJ0401000
• Journal Information: Journal of Computational Physics, 243:323-343, Journal Name: Journal of Computational Physics, 243:323-343
• Country of Publication: United States
• Language: English

Related Subjects

PDF methods
Uncertainty quantification
Heterogeneous reaction
Stochastic modeling