Error using pdepe (line 293) Spatial discretization has failed.

2018 9 19
1 个回答
回答已采纳
更新时间：2018 9 20
9 次查看（30 天）

0 个投票

I keep getting following error for my code. not sure where I went wrong.
Error using pdepe (line 293) Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.
Error in Kronstadt_HW4_problem3_pdepe (line 28) sol=pdepe(m,pdepb,@pbIC,pbBC,x,t,options); %solution
function Kronstadt_HW4_problem3_pdepe
%This is a dimensional formulation
close all
Nx=201; %number of points in x direction
Nt=101; %number of points in time
m=0; %cartesian
D=2.4E-9; %m^2/s, diffusivity
Na=0.025; %mol/m^3-s, sink
Ci=0.04; %mol/m^3, initial condition
Cw = 0.04; %mol/m^3, this is the set concentration at the right boundary
Xmax=.1; %m
tmax=1000000; %sec
dx=Xmax/(Nx-1);
dt=tmax/(Nt-1);
t=linspace(0,tmax,Nt);
x=linspace(0,Xmax,Nx);
options=odeset; %('MaxStep',100);
%anonymous functions to pass parameters
pbBC=@(yl,Cl,yr,Cr,t)pbBC1(yl,Cl,yr,Cr,t,Cw);
pdepb=@(x,t,C,DCDx)pdepb1(x,t,C,DCDx,Na,D);
sol=pdepe(m,pdepb,@pbIC,pbBC,x,t,options); %solution
C=sol(:,:,1); %extract solution
x_value1=6;
x_value2=16;
x_value3=36;
x_value4=51;
plot(t,C(:,x_value1),t,C(:,x_value2),t,C(:,x_value3),t,C(:,x_value4)) %Plot vs t at specified x locations
xlabel('Time (s)')
ylabel('Concentration (mol/m^3)')
legend([num2str(x_value1*dx-dx) ' m'],[num2str(x_value2*dx-dx) ' m'],[num2str(x_value3*dx-dx) ' m'],[num2str(x_value4*dx-dx) ' m'])
figure(2) %Plot vs x at specified times
t1=2;
t2=11;
t3=31;
t4=101;
plot(x,C(t1,:),x,C(t2,:),x,C(t3,:),x,C(t4,:))
xlabel('x (m)')
ylabel('Concentration (mol/m^3)')
ylim([0 Cw])
xlim([0 Xmax])
legend([num2str(t1*dt-dt) ' sec'],[num2str(t2*dt-dt) ' sec'],[num2str(t3*dt-dt) ' sec'], [num2str(t4*dt-dt) ' sec'])
figure(3) %Flux at both wall surfaces
flux_l=-D*(C(:,2)-C(:,1))/dx; %mol/s-m
flux_r=-D*(C(:,Nx)-C(:,Nx-1))/dx; %mol/s-m
plot(t,flux_l,t,flux_r)
legend('Flux (left wall)','Flux (right wall)')
xlabel('Time (sec)')
ylabel('Mass Flux (mol/s-m^2)')
ylim([0 .5E-8])
figure(4) %Flux at both left surface
semilogy(t,flux_l)
legend('Flux (left wall)')
xlabel('Time (sec)')
ylabel('Mass Flux (mol/s-m^2)')
grid on
figure(5)
Ns=5;
ta=linspace(0,tmax,(Nt-1)/Ns);
xa=linspace(0,Xmax,(Nx-1)/Ns);
[X,T]=meshgrid(xa,ta);
for i=1:length(ta)
for j=1:length(xa)
C1(i,j)=C(1+i*Ns,1+j*Ns);
end
end
surface(X,T,C1)
ylabel('Time (s)')
xlabel('Position (m)')
zlabel('Concentration (mol/m^3)')
function [c,f,s]=pdepb1(x,t,C,DCDx,Na,D) %define pde system – see Matlab help for pdepe
c=1; %coefficient on time derivative
f=D*DCDx; %general flux mol/s-m^3 (negative of diffusive flux)
s=Na; %sink mol/s-m^3
function C0=pbIC(x) %initial condition
C0=0.04; %mol/m^3
function [pl,ql,pr,qr]=pbBC1(yl,Cl,yr,Cr,t,Cw) %boundary conditions
pl=0; %left side bc. This one sets flux to zero since the left side is impermeable
ql=1; %Form is pl + ql*f = 0 where f is flux from definition of pde system in function pdepb
pr=Cl-Cw; %right side bc. This one sets concentration to Cw
qr=0;

请先登录，再回答此问题。

 采纳的回答

Torsten
Torsten 2018-9-19

2 个投票

Try
function Kronstadt_HW4_problem3_pdepe
%This is a dimensional formulation
close all
Nx=201; %number of points in x direction
Nt=101; %number of points in time
m=0; %cartesian
D=2.4E-9; %m^2/s, diffusivity
Na=0.025; %mol/m^3-s, sink
Ci=0.04; %mol/m^3, initial condition
Cw = 0.04; %mol/m^3, this is the set concentration at the right boundary
Xmax=.1; %m
tmax=1000000; %sec
dx=Xmax/(Nx-1);
dt=tmax/(Nt-1);
t=linspace(0,tmax,Nt);
x=linspace(0,Xmax,Nx);
options=odeset; %('MaxStep',100);
%anonymous functions to pass parameters
pbBC=@(yl,Cl,yr,Cr,t)pbBC1(yl,Cl,yr,Cr,t,Cw);
pbIC = @(x)pbIC1(x,Xmax,Cw);
pdepb=@(x,t,C,DCDx)pdepb1(x,t,C,DCDx,Na,D);
sol=pdepe(m,pdepb,pbIC,pbBC,x,t,options); %solution
C=sol(:,:,1); %extract solution
x_value1=6;
x_value2=16;
x_value3=36;
x_value4=51;
plot(t,C(:,x_value1),t,C(:,x_value2),t,C(:,x_value3),t,C(:,x_value4)) %Plot vs t at specified x locations
xlabel('Time (s)')
ylabel('Concentration (mol/m^3)')
legend([num2str(x_value1*dx-dx) ' m'],[num2str(x_value2*dx-dx) ' m'],[num2str(x_value3*dx-dx) ' m'],[num2str(x_value4*dx-dx) ' m'])
figure(2) %Plot vs x at specified times
t1=2;
t2=11;
t3=31;
t4=101;
plot(x,C(t1,:),x,C(t2,:),x,C(t3,:),x,C(t4,:))
xlabel('x (m)')
ylabel('Concentration (mol/m^3)')
ylim([0 Cw])
xlim([0 Xmax])
legend([num2str(t1*dt-dt) ' sec'],[num2str(t2*dt-dt) ' sec'],[num2str(t3*dt-dt) ' sec'], [num2str(t4*dt-dt) ' sec'])
figure(3) %Flux at both wall surfaces
flux_l=-D*(C(:,2)-C(:,1))/dx; %mol/s-m
flux_r=-D*(C(:,Nx)-C(:,Nx-1))/dx; %mol/s-m
plot(t,flux_l,t,flux_r)
legend('Flux (left wall)','Flux (right wall)')
xlabel('Time (sec)')
ylabel('Mass Flux (mol/s-m^2)')
ylim([0 .5E-8])
figure(4) %Flux at both left surface
semilogy(t,flux_l)
legend('Flux (left wall)')
xlabel('Time (sec)')
ylabel('Mass Flux (mol/s-m^2)')
grid on
figure(5)
Ns=5;
ta=linspace(0,tmax,(Nt-1)/Ns);
xa=linspace(0,Xmax,(Nx-1)/Ns);
[X,T]=meshgrid(xa,ta);
for i=1:length(ta)
for j=1:length(xa)
C1(i,j)=C(1+i*Ns,1+j*Ns);
end
end
surface(X,T,C1)
ylabel('Time (s)')
xlabel('Position (m)')
zlabel('Concentration (mol/m^3)')
function [c,f,s]=pdepb1(x,t,C,DCDx,Na,D) %define pde system – see Matlab help for pdepe
c=1; %coefficient on time derivative
f=D*DCDx; %general flux mol/s-m^3 (negative of diffusive flux)
s=Na; %sink mol/s-m^3
function C0=pbIC1(x,Xmax,Cw) %initial condition
if x==Xmax
C0=Cw;
else
C0=0.04; %mol/m^3
end
function [pl,ql,pr,qr]=pbBC1(yl,Cl,yr,Cr,t,Cw) %boundary conditions
pl=0; %left side bc. This one sets flux to zero since the left side is impermeable
ql=1; %Form is pl + ql*f = 0 where f is flux from definition of pde system in function pdepb
pr=Cr-Cw; %right side bc. This one sets concentration to Cw
qr=0;

2 个评论
显示 无 隐藏 无

of course I forgot all about my initial condition! Thank you so much!
Torsten
Torsten 2018-9-20
The main problem was that you set
pr=Cl-Cw;
instead of
pr=Cr-Cw;
Best wishes
Torsten.

请先登录，再进行评论。

更多回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Eigenvalue Problems 的更多信息

产品

版本

R2018a

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by