#
Appendix D:

##
Steady State Matrix Coefficients

The purpose of this appendix is to develop the matrix coefficients
(*E*, *F*, *G*) and the forcing function
(*R*) from Equation (26). In the text that follows, the
contributions to *E*, *F*, *G* and
*R* are given on a term-by-term basis. The final values are
determined by summing the individual contributions.

## D1.0 Advection

Equations (B7), (B11), and (B17) are used to approximate the spatial
derivative describing advective transport. These equations
contribute to the matrix coefficients as detailed below. Due to
boundary conditions, the contributions depend on the type of segment
for which Equation (26) is developed.

### Interior Segments

(D1)
(D2)

(D3)

### First Segment

(D4)
(D5)

(D6)

### Last Segment

(D7)
(D8)

(D9)

## D2.0 Dispersion

As with the advection term, the finite difference equations given
in Appendix B (Equations (B9), (B14) and (B18)) are used to
determine the contributions to the matrix coefficients.

### Interior Segments

(D10)
(D11)

(D12)

### First Segment

(D13)
(D14)

(D15)

### Last Segment

(D16)
(D17)

(D18)

## D3.0 Lateral Inflow

(D19)
(D20)

## D4.0 Transient Storage

(D21)
(D22)

## D5.0 Decay

(D23)

## D6.0 Matrix Coefficients

The matrix coefficients (*E*, *F*, *G*) and
the forcing function (*R*) from Equation (26) may
now be developed by summing the contributions given in Sections D1.0
through D5.0;

(D24)
(D25)

(D26)

(D27)