# ADE1Danalytical

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Returns a concentration profile for each point in x as function of time t

Version : 1.0

Author : George Kourakos

email: giorgk@gmail.com

web : http://groundwater.ucdavis.edu/msim

Date 28-Mar-2014

Department of Land Air and Water

University of California Davis

## Contents

## Usage

C = ADE1Danalytical(x, t, v, cf, aL, Dm, lambda, R)

## Input

* x*: points in 1D domain where we want to compute the breakthrough curve

* t*: times where the concentration will be computed

* v*: pore velocity i.e. v=V/porosity

* cf*: Input concentration

* aL*: Longitudinal dispersion coefficient

* Dm*: Molecular diffusion coefficient

* lambda*: Decay constant

* R*: Retardation factor

## Output:

* C*: [NtxNp] matrix where Nt is the number of time steps and Np is the points where we want to compute the breakthrough

## Example:

In the following example we will compute the breakthrough curve for 200 years of transport along a 10 km path, which is a quite common in non-point source pollution. The velocity is 0.3 m/day. The concentration profiles will be computed at yearly basis.

Dm = 1e-7; R = 1; aL = 1000; cf = 1; lambda = 0; x = 1:100:10000; t = [0:200]*365; v = 0.3; C = ADE1Danalytical(x,t,v,cf,aL,Dm,lambda,R); surf(x/1000,t/365,C,'edgecolor','none') title ('Concentration profile') xlabel('x [km]') ylabel('Time [years]') view(0,90)