Anti-Diffusion Modeling using a Non-local Censored ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Anti-Diffusion Modeling using a Non-local Censored Random Walk Scheme
Paper
Author:Amvrossios Bagtzoglou <acb@engr.uconn.edu> (Department of Civil & Environmental Engineering, University of Connecticut)
Rachid Ababou <ababou@imft.fr> (Institut de Mecanique des Fluides, INP de Toulouse - ENSEEIHT)
Presenter:Amvrossios Bagtzoglou <acb@engr.uconn.edu> (Department of Civil & Environmental Engineering, University of Connecticut)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000343
DOI:10.4122/1.1000000344

This paper builds on the Reversed Time Particle Tracking Method of Bagtzoglou (2003) and presents a novel methodology for time reversal in groundwater transport simulations. The basis of the proposed scheme for anti-diffusion is a continuous time, censored, nonlocal random walk capable of tracking groundwater solute concentration profiles over time. Our analysis leads to the conclusion that an adaptive (decreasing) time-stepping scheme is necessary in order to maintain a constant amount of anti-diffusion. More specifically, we study the interrelations between the following parameters: time-step evolution versus time or number of steps; variance evolution (decrease rate); and total time or total number of steps required to reach a fully anti-diffused solution. The approach is shown to be quite efficient (every 80 time steps an eight-fold reduction of the variance is attained) and is also asymptotically exact. Our method is applied to one-dimensional transport of conservative solutes in spatially invariant and variant groundwater flow fields with great success.