Adaptive Fup multi-resolution approach to flow and advective transport in highly heterogeneous porous media: Methodology, accuracy and convergence
2009 (English)In: Advances in Water Resources, ISSN 0309-1708, E-ISSN 1872-9657, Vol. 32, no 6, 885-905 p.Article in journal (Refereed) Published
In this paper, we present a new Monte-Carlo methodology referred to as Adaptive Fup Monte-Carlo Method (AFMCM) based on compactly supported Fup basis functions and a multi-resolution approach. We consider for illustration 2-D steady, linear and unidirectional flow and advective transport defined on a domain of size 64I(Y) * 32I(Y) with isotropic exponential correlation heterogeneity structure and sigma(2)(Y) up to 8. Accuracy and convergence issues are rigorously analyzed for each realization as well as for the ensemble. Log-conductivity is presented by continuous function at high resolution level (n(Y) = 4-32 points per integral scale) reproducing very accurately prescribed statistics. The flow problem is the most demanding Monte-Carlo step due to satisfying detailed log-conductivity properties. Presented methodology inherently gives continuous and mesh-free velocity fields, which enables the construction of a new efficient and accurate particle tracking algorithm. Results indicate that resolutions n(Y) = 8 and n(h) = 32 enable very accurate flow solutions in each realization with mass balance error less than 3% and accurate ensemble velocity statistics. Results show that the proposed AFMCM enables tracking of an unlimited number of injected particles and calculates required transport variables as continuous functions with desired relative accuracy (0.1%) in each realization. Furthermore, we show that the resolution n(Y) = 8 yields a quite accurate pdf of the transverse displacement and travel time. All required flow and transport variables require 500 Monte-Carlo realizations in order to stabilize fluctuations of the higher-order moments and the probability density functions.
Place, publisher, year, edition, pages
2009. Vol. 32, no 6, 885-905 p.
Adaptive multi-resolution approach, Flow and advective transport, Highly heterogeneous porous media, Fup basis functions, Monte-Carlo, method, Particle tracking, wavelet collocation method, solute flux approach, groundwater-flow, atomic functions, 1st-order approximations, stochastic-analysis, elliptic problems, log-conductivity, finite-elements, path lines
IdentifiersURN: urn:nbn:se:kth:diva-18506DOI: 10.1016/j.advwatres.2009.02.013ISI: 000266895000009ScopusID: 2-s2.0-67349160471OAI: oai:DiVA.org:kth-18506DiVA: diva2:336553
QC 201005252010-08-052010-08-052011-08-30Bibliographically approved