A PDE equation giving meaningless results
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Dursman Mchabe
on 19 Sep 2018
Commented: Dursman Mchabe
on 19 Sep 2018
Hi Everyone,
I am trying to solve a simpe PDE equation using pdepe, however I get meaningless results. Please see the code below. I don't know where could I be going wrong. The equations are:
% simple PDE % Equation: dC/dt = K * d^2C/dx^2 - kr * C
% IC: C0 = 0.762471166
% BC: x = 0, t > 0, C = Cfinal
% BC: x = delta, t > 0, C = 0
The code looks like this:
function SimplePDE
% simple PDE
% Equation: dC/dt = K * d^2C/dx^2 - kr * C
% IC: C0 = 0.762471166
% BC: x = 0, t > 0, C = Cfinal
% BC: x = delta, t > 0, C = 0
global K kr kl dp delta
K = 1.1e-8;
kr = 4.16e-5;
kl = 9.93e-3;
dp = 3.64e-5;
delta = (dp * K)/(2 - kl * dp);
m = 0;
x = linspace(0,delta,100);
t = linspace(0,30,100);
sol = pdepe(m,@DRpde,@DRic,@DRbc,x,t);
C = sol(:,:,1);
figure, plot(t,C(:,1),'r--')
xlabel('Time (sec)')
ylabel('Conc (mol/m^{3})')
hold on
%%EXPERIMENTAL
time = [1;
3;
5;
7;
9;
11;
13;
15;
17;
19;
21;
23;
25;
27;
29;
];
Conc = [0.762471166
0.630957344
0.10964782
0.051286138
0.027542287
0.020417379
0.014791084
0.010715193
0.009120108
0.007943282
0.00691831
0.006309573
0.005623413
0.005128614
0.004897788
];
plot(time, Conc,'bv', 'markersize',6,'markerfacecolor','b')
xlabel('Time (sec)')
ylabel('Conc H^+ (mol/m^3)')
hold off
% --------------------------------------------------------------
figure, surf(x,t,C)
zlabel('Time (sec)')
xlabel('Conc (mol/m^{3})')
ylabel('Boundary Layer Thickness (m)')
% --------------------------------------------------------------
function [c,f,s] = DRpde(x,t,C,DCDx)
global K kr
c = 1;
f = K * DCDx;
s = -kr * C;
% --------------------------------------------------------------
function C0 = DRic(x)
C0 = 0.762471166;
% --------------------------------------------------------------
function [pl,ql,pr,qr] = DRbc(xl,Cl,xr,Cr,t)
pl = Cl;
ql = 0;
pr = Cr;
qr = 0;
0 Comments
Accepted Answer
Torsten
on 19 Sep 2018
Try
function main
% simple PDE
% Equation: dC/dt = K * d^2C/dx^2 - kr * C
% IC: C0 = 0.762471166
% BC: x = 0, t > 0, C = Cfinal
% BC: x = delta, t > 0, C = 0
global K kr kl dp delta Cfinal
K = 1.1e-8;
kr = 4.16e-5;
kl = 9.93e-3;
dp = 3.64e-5;
delta = (dp * K)/(2 - kl * dp)
Cfinal = 0.3;
m = 0;
x = linspace(0,delta,100);
t = linspace(0,1e-18,8);
sol = pdepe(m,@DRpde,@DRic,@DRbc,x,t);
C = sol(:,:,1);
plot(x,C(1,:),x,C(2,:),x,C(3,:),x,C(4,:),x,C(5,:))
zlabel('Time (sec)')
xlabel('Conc (mol/m^{3})')
ylabel('Boundary Layer Thickness (m)')
% --------------------------------------------------------------
function [c,f,s] = DRpde(x,t,C,DCDx)
global K kr
c = 1;
f = K * DCDx;
s = -kr * C;
% --------------------------------------------------------------
function C0 = DRic(x)
global delta Cfinal
if x==0
C0 = Cfinal;
elseif x==delta
C0 = 0;
else
C0 = 0.762471166;
end
% --------------------------------------------------------------
function [pl,ql,pr,qr] = DRbc(xl,Cl,xr,Cr,t)
global Cfinal
pl = Cl - Cfinal;
ql = 0;
pr = Cr;
qr = 0;
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