Assigment due: March 5, 2012
Two groups:
Group 1:
Develop a MATLAB program that solves the eective conductivity problem
for 2-D problems for a broad range of periodic variability. Method: FourierGaler
Selected Web Resources for Fourier Analysis
Web Book by Julius O. Smith
Web Book by Paolo Prandoni and Martin Vetterli
Tables of Transform Pairs by Marc Stoecklin
CN
Chapter 4
CT
Stokes Flow and Darcys Law
In this chapter, we will focus on the linearized ow equations that describe creeping ow.
We examine the fundamental equations of uid mechanics in order to bu
The Virtual Laboratory Approach
In this approach we imitate through mathematical simulation the process of
evaluating eective parameters of a block of a heterogeneous porous medium.
This approach give
Chapter 0
Taylor Dispersion
We will examine a classical upscaling problem, known as Taylor dispersion.
This problem is interesting and sustantial in itself but it becomes even more
important when we c
WATER RESOURCES
RESEARCH,
VOL. 19, NO. 1, PAGES 161-180, FEBRUARY
1983
Three-Dimensional Stochastic Analysis of Macrodispersion
in Aquifers
LYNN W. GELHAR1 AND CARL L. AXNESS
2
New Mexico Institute of
WATER RESOURCES RESEARCH,
VOL. 25, NO. 11, PAGES 2287-2298, NOVEMBER
1989
Numerical Spectral Approach for the Derivation
of Piezometric
THOMAS
VAN
Head
LENT
Covariance
Functions
AND PETER K. KITANIDIS
WATER RESOURCES
RESEARCH,
VOL. 32, NO. 5, PAGES 1197-1207, MAY 1996
Effects of first-order approximations on head and specific
discharge covariancesin high-contrast log conductivity
Thomas
Van Lent
De
function [ran,x] = rfld1d(n,dx,rcovar);
% RFLD1D: Computes a realization of a 1-dimensional stationary
% random field
%
% Call by:
% [ran,x] = rfld1d(n,dx,rcovar)
% Input:
% n - number of nodes at whi
Chapter 0
Review of Stochastic
Processes
In this chapter we will review some useful denitions and concepts from stochastic processes. When stochastic processes are functions (particularly functions
of
Selected Web Resources for Fourier Analysis
Web Book by Julius O. Smith
Web Book by Paolo Prandoni and Martin Vetterli
Tables of Transform Pairs by Marc Stoecklin
January 11, 2012
6:20
World Scienti c Book - 9.75in x 6.5in
Chapter 1
Introduction
In this chapter, we dene the scope of these notes and introduce some key concepts.
1.1
Objectives
Porous media and, m
EffectiveConductivity
A series of three papers:
Kitanidis, P. K., "Effective Hydraulic Conductivity for Gradually Varying Flow." Water
Resources Research, 26(6), 1197-1208, 1990.
Dykaar, B. B., and Ki
The DFT
In our introduction to the numerical spectral approach, we encountered some of
the numerical challenges of computing Fourier coecients and periodic functions
from Fourier coecients. This leads
Chapter 0
Fourier Series
Fourier analysis is invaluable in the study of heterogeneity. The simplest application and a good place to start is with periodic media where Fourier-series
analysis applies.
Chapter 0
Multi-dimensional Fourier
In most applications, we are interested in variability in two or three dimensions.
Extension of Fourier series and integral to higher dimensions is simple, provided
Review of Stieltjes Integrals
P. K. Kitanidis
February 15, 2012
The Riemann-Stieltjes Integral
Consider an interval [ ] and the partition
= cfw_ = 0 1 =
(1)
The norm (or mesh) of the partition is th
Chapter 0
Fourier Integral
The Fourier series describes variability in a nite interval, with periodic repetition assumed for outside of that interval, and is convenient to use in numerical
computation
Review of Gelhar and Axness Approach
P. K. Kitanidis
February 22, 2012
For steady ow with isotropic but nonuniform conductivity = (x) 0:
=0
(1)
which is the same as
ln
2
+
=0
(2)
ln = + , = [ln
D ecember 29, 2011
13:23
World Scientic Book - 9.75in x 6.5in
Preface
This is a set of class notes for a specialized course on the eects of heterogeneity and
scale on ow and transport in permeable for
function [ran,x,y] = rfld2d(n,dx,rcovar)
% RFLD2D: Generates a realization of a 2-dimensional intrinsic
% random field
% function [ran,x,y] = rfld2d(n,dx,rcovar)
% Inputs:
% n - vector with number of