Dynamics of free surfaces in random porous media

Daniel M. Tartakovsky, C Larrabee Winter

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We consider free surface flow in random porous media by treating hydraulic conductivity of a medium as a random field with known statistics. We start by recasting the boundary-value problem in the form of an integral equation where the parameters and domain of integration are random. Our analysis of this equation consists of expanding the random integrals in Taylor's series about the mean position of the free boundary and taking the ensemble mean. To quantify the uncertainty associated with such predictions, we also develop a set of integro-differential equations satisfied by the corresponding second ensemble moments. The resulting moment equations require closure approximations to be workable. We derive such closures by means of perturbation expansions in powers of the variance of the logarithm of hydraulic conductivity. Though this formally limits our solutions to mildly heterogeneous porous media, our analytical solutions for one-dimensional flows demonstrate that such perturbation expansions may remain robust for relatively large values of the variance of the logarithm of hydraulic conductivity.

Original languageEnglish (US)
Pages (from-to)1857-1876
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume61
Issue number6
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Hydraulic Conductivity
Hydraulic conductivity
Free Surface
Porous Media
Porous materials
Perturbation Expansion
Logarithm
Closure
Ensemble
Heterogeneous Porous Media
Moment Equations
Free Surface Flow
Integrodifferential equations
Taylor series
Free Boundary
Integro-differential Equation
Random Field
Boundary value problems
Integral equations
Integral Equations

Keywords

  • Moment equations
  • Moving boundary
  • Porous media
  • Random
  • Stochastic

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Dynamics of free surfaces in random porous media. / Tartakovsky, Daniel M.; Winter, C Larrabee.

In: SIAM Journal on Applied Mathematics, Vol. 61, No. 6, 2001, p. 1857-1876.

Research output: Contribution to journalArticle

Tartakovsky, Daniel M. ; Winter, C Larrabee. / Dynamics of free surfaces in random porous media. In: SIAM Journal on Applied Mathematics. 2001 ; Vol. 61, No. 6. pp. 1857-1876.
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