Premium
Efficient stochastic finite element methods for flow in heterogeneous porous media. Part 2: Random lognormal permeability
Author(s) -
Traverso Luca,
Phillips Timothy Nigel
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4842
Subject(s) - polynomial chaos , mathematics , random field , finite element method , porous medium , nonlinear system , preconditioner , stochastic process , random variable , mathematical analysis , polynomial , iterative method , monte carlo method , mathematical optimization , physics , porosity , statistics , geotechnical engineering , quantum mechanics , thermodynamics , engineering
Summary Efficient and robust iterative methods are developed for solving the linear systems of equations arising from stochastic finite element methods for single phase fluid flow in porous media. Permeability is assumed to vary randomly in space according to some given correlation function. In the companion paper, herein referred to as Part 1, permeability was approximated using a truncated Karhunen‐Loève expansion (KLE). The stochastic variability of permeability is modeled using lognormal random fields and the truncated KLE is projected onto a polynomial chaos basis. This results in a stochastic nonlinear problem since the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Symmetric block Gauss‐Seidel used as a preconditioner for CG is shown to be efficient and robust for stochastic finite element method.