Unable to correct the code. Error shows the ode45 does not give a column vector. Please help me with these.

2 views (last 30 days)
clear all, close all, clc
%nu=0.001; % Diffusion constant
g1 = 9.81;
J = 1.2./1000;
h = 0.075;
lambda = 0.075;
u_star = sqrt(g1.*J.*h);
%%Pressure term %%
P = (9.*u_star.^2)./h;
nu = 10^(-6)./(u_star.*h);
a = 0.4;
XXx = 0:0.01:1;
YYx = (XXx.*(1-XXx))./(1+12.*0.19.*XXx.^2.*(1-XXx));
FF = trapz(XXx,YYx);
nu_t = a.*FF;
% Define spatial domain
Lx = 2; % Length of domain
Ly = 2;
N = 200; % Number of discretization points
M = 200;
dx = Lx/N;
dy = Ly/M;
x = -Lx/2:dx:Lx/2-dx; % Define x domain
y = -Ly/2:dy:Ly/2-dy;
[X,Y] = meshgrid(x,y);
% Define discrete wavenumbers
eta = (2*pi/Lx)*[-N/2:N/2-1];
eta = fftshift(eta'); % Re-order fft wavenumbers
jeta = (2*pi/Ly)*[-M/2:M/2-1];
jeta = fftshift(jeta'); % Re-order fft wavenumbers
[Eta,Jeta] = meshgrid(eta,jeta);
% Initial condition
u0 = sin(pi.*X).*sin(pi.*Y);
% Simulate PDE in spatial domain
dt = 0.01;
t = 0:dt:(2-0.01);
[t,s] = ode45(@(t,s)rhsBurgers(t,s,Eta,Jeta,nu,nu_t),t,u0)
ddpsidtdy =
1.0e+08 * 0.0000 + 0.0000i 0.0005 - 0.0000i 0.0010 - 0.0000i 0.0015 - 0.0000i 0.0020 + 0.0000i 0.0025 + 0.0001i 0.0030 + 0.0002i 0.0035 + 0.0004i 0.0040 + 0.0007i 0.0045 + 0.0010i 0.0050 + 0.0015i 0.0055 + 0.0020i 0.0060 + 0.0026i 0.0065 + 0.0034i 0.0070 + 0.0043i 0.0075 + 0.0053i 0.0080 + 0.0065i 0.0085 + 0.0079i 0.0090 + 0.0094i 0.0095 + 0.0111i 0.0101 + 0.0130i 0.0106 + 0.0151i 0.0111 + 0.0174i 0.0117 + 0.0200i 0.0122 + 0.0228i 0.0127 + 0.0258i 0.0133 + 0.0290i 0.0138 + 0.0326i 0.0144 + 0.0364i 0.0149 + 0.0405i 0.0155 + 0.0449i 0.0161 + 0.0496i 0.0166 + 0.0546i 0.0172 + 0.0600i 0.0178 + 0.0656i 0.0184 + 0.0717i 0.0190 + 0.0780i 0.0196 + 0.0848i 0.0202 + 0.0919i 0.0208 + 0.0994i 0.0214 + 0.1074i 0.0220 + 0.1157i 0.0227 + 0.1244i 0.0233 + 0.1336i 0.0240 + 0.1432i 0.0246 + 0.1533i 0.0253 + 0.1638i 0.0259 + 0.1748i 0.0266 + 0.1862i 0.0273 + 0.1982i 0.0280 + 0.2106i 0.0287 + 0.2236i 0.0294 + 0.2371i 0.0301 + 0.2511i 0.0308 + 0.2657i 0.0315 + 0.2808i 0.0323 + 0.2965i 0.0330 + 0.3127i 0.0338 + 0.3296i 0.0346 + 0.3470i 0.0353 + 0.3650i 0.0361 + 0.3837i 0.0369 + 0.4029i 0.0377 + 0.4228i 0.0385 + 0.4434i 0.0394 + 0.4646i 0.0402 + 0.4864i 0.0411 + 0.5090i 0.0419 + 0.5322i 0.0428 + 0.5561i 0.0437 + 0.5807i 0.0446 + 0.6061i 0.0455 + 0.6321i 0.0464 + 0.6589i 0.0473 + 0.6865i 0.0482 + 0.7148i 0.0492 + 0.7439i 0.0501 + 0.7737i 0.0511 + 0.8043i 0.0521 + 0.8358i 0.0531 + 0.8680i 0.0541 + 0.9011i 0.0551 + 0.9350i 0.0562 + 0.9697i 0.0572 + 1.0053i 0.0583 + 1.0417i 0.0594 + 1.0790i 0.0605 + 1.1172i 0.0616 + 1.1563i 0.0627 + 1.1963i 0.0638 + 1.2372i 0.0650 + 1.2790i 0.0662 + 1.3217i 0.0673 + 1.3654i 0.0685 + 1.4100i 0.0697 + 1.4556i 0.0710 + 1.5022i 0.0722 + 1.5497i 0.0735 + 1.5983i 0.0747 + 1.6478i -0.0763 - 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Error using odearguments (line 93)
@(T,S)RHSBURGERS(T,S,ETA,JETA,NU,NU_T) must return a column vector.

Error in ode45 (line 106)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
W_wc = sin(pi.*Y).*sin(pi.*X);
%% FIGURES (PRODUCTION)
figure(1)
plot(x,real(psi(1,:)),'-')
hold on
title('r')
xlabel('y'), ylabel('z')
plot(x,W_wc,'--')
axis([-1 1 0 1])
function ddpsidtdy = rhsBurgers(t,s,eta,jeta,nu,nu_t)
% uhat = fft(u);
% duhat = i*eta.*uhat;
% dduhat = -(eta.^2).*uhat;
% du = ifft(duhat);
% ddu = ifft(dduhat);
% dudt = -u.*du + nu*ddu;
h = 0.075;
g1 = 9.81;
J = 1.2./1000;
s = fft(s);
u_star = sqrt(g1.*J.*h);
drhatdy = 1i*eta.*s(1);
drhatdz = 1i*jeta.*s(1);
ddrhatdydy = -eta.^2.*s(1);
ddrhatdzdz = -jeta.^2.*s(1);
ddrhatdydz = -jeta.*eta.*s(1);
drdy = ifft(drhatdy);
drdz = ifft(drhatdz);
ddrdydy = ifft(ddrhatdydy);
ddrdzdz = ifft(ddrhatdzdz);
ddrdydz = ifft(ddrhatdydz);
drdt = -(s(2).*drdy) -(s(1).*drdz)-(g1*J)+(nu.*(ddrdydy+ddrdzdz))+ (nu_t.*(ddrdydy-ddrdzdz+ddrdydz));
%%%% Using stream function %%%%%
dpsidy = s(1); %%%%% r %%%%
dpsidz = -s(2); %%%%% q %%%%
ddpsidydy = ifft(-eta.^2.*s(1));
ddpsidzdz = ifft(-jeta.^2.*s(2));
ddpsidydz = ifft(-jeta.*eta.*s(2));
dddpsidzdzdz = ifft(-1i.*eta.^3.*s(2));
dddpsidydydz = ifft(-1i.*eta.^2.*jeta.*s(2));
dddpsidzdzdy = ifft(-1i.*jeta.^2.*eta.*s(1));
ddpsidtdy = -(dpsidz.*ddpsidydz)-(dpsidy.*ddpsidzdz)+(9.*u_star.^2./h)-((nu+nu_t).*(dddpsidydydz+dddpsidzdzdz))-(nu_t.*dddpsidzdzdy)
end
  2 Comments
Titas Chattopadhyay
Titas Chattopadhyay on 27 Dec 2021
Thank you for your answer. But, I have already written it into the presciribed one. Can you tell me how to resolve this issue?

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Accepted Answer

Walter Roberson
Walter Roberson on 27 Dec 2021
Edited: Walter Roberson on 27 Dec 2021
The below calculation takes a long time. Eventually it will fail because you try to plot psi which does not exist. You do not use the output of your ode45 call in your plotting.
The u0 boundary condition you pass in is 200 x 200. Inside the function the current conditions are in the variable s which will always be received as a column vector because MATLAB reshapes the conditions to a column. You proceed to do fft() of that column vector. I have to wonder whether perhaps you thought that you were dealing with a 200 x 200 array at that point.
I also wonder whether the equations happen to be "stiff", if you might need to use ode23s() instead.
clear all, close all, clc
%nu=0.001; % Diffusion constant
g1 = 9.81;
J = 1.2./1000;
h = 0.075;
lambda = 0.075;
u_star = sqrt(g1.*J.*h);
%%Pressure term %%
P = (9.*u_star.^2)./h;
nu = 10^(-6)./(u_star.*h);
a = 0.4;
XXx = 0:0.01:1;
YYx = (XXx.*(1-XXx))./(1+12.*0.19.*XXx.^2.*(1-XXx));
FF = trapz(XXx,YYx);
nu_t = a.*FF;
% Define spatial domain
Lx = 2; % Length of domain
Ly = 2;
N = 200; % Number of discretization points
M = 200;
dx = Lx/N;
dy = Ly/M;
x = -Lx/2:dx:Lx/2-dx; % Define x domain
y = -Ly/2:dy:Ly/2-dy;
[X,Y] = meshgrid(x,y);
% Define discrete wavenumbers
eta = (2*pi/Lx)*[-N/2:N/2-1];
eta = fftshift(eta'); % Re-order fft wavenumbers
jeta = (2*pi/Ly)*[-M/2:M/2-1];
jeta = fftshift(jeta'); % Re-order fft wavenumbers
[Eta,Jeta] = meshgrid(eta,jeta);
% Initial condition
u0 = sin(pi.*X).*sin(pi.*Y);
% Simulate PDE in spatial domain
dt = 0.05;
t = 0:dt:(2-0.01);
[t,s] = ode45(@(t,s)rhsBurgers(t,s,Eta,Jeta,nu,nu_t),t,u0)
W_wc = sin(pi.*Y).*sin(pi.*X);
%% FIGURES (PRODUCTION)
figure(1)
plot(x,real(psi(1,:)),'-')
hold on
title('r')
xlabel('y'), ylabel('z')
plot(x,W_wc,'--')
axis([-1 1 0 1])
function ddpsidtdy = rhsBurgers(t,s,eta,jeta,nu,nu_t)
% uhat = fft(u);
% duhat = i*eta.*uhat;
% dduhat = -(eta.^2).*uhat;
% du = ifft(duhat);
% ddu = ifft(dduhat);
% dudt = -u.*du + nu*ddu;
h = 0.075;
g1 = 9.81;
J = 1.2./1000;
s = fft(s);
u_star = sqrt(g1.*J.*h);
drhatdy = 1i*eta.*s(1);
drhatdz = 1i*jeta.*s(1);
ddrhatdydy = -eta.^2.*s(1);
ddrhatdzdz = -jeta.^2.*s(1);
ddrhatdydz = -jeta.*eta.*s(1);
drdy = ifft(drhatdy);
drdz = ifft(drhatdz);
ddrdydy = ifft(ddrhatdydy);
ddrdzdz = ifft(ddrhatdzdz);
ddrdydz = ifft(ddrhatdydz);
drdt = -(s(2).*drdy) -(s(1).*drdz)-(g1*J)+(nu.*(ddrdydy+ddrdzdz))+ (nu_t.*(ddrdydy-ddrdzdz+ddrdydz));
%%%% Using stream function %%%%%
dpsidy = s(1); %%%%% r %%%%
dpsidz = -s(2); %%%%% q %%%%
ddpsidydy = ifft(-eta.^2.*s(1));
ddpsidzdz = ifft(-jeta.^2.*s(2));
ddpsidydz = ifft(-jeta.*eta.*s(2));
dddpsidzdzdz = ifft(-1i.*eta.^3.*s(2));
dddpsidydydz = ifft(-1i.*eta.^2.*jeta.*s(2));
dddpsidzdzdy = ifft(-1i.*jeta.^2.*eta.*s(1));
ddpsidtdy = -(dpsidz.*ddpsidydz)-(dpsidy.*ddpsidzdz)+(9.*u_star.^2./h)-((nu+nu_t).*(dddpsidydydz+dddpsidzdzdz))-(nu_t.*dddpsidzdzdy);
ddpsidtdy = ddpsidtdy(:);
end
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