Unable to correct the code. Error shows the ode45 does not give a column vector. Please help me with these.
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Titas Chattopadhyay
2021-12-27
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 *
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Error using odearguments (line 93)
@(T,S)RHSBURGERS(T,S,ETA,JETA,NU,NU_T) must return a column vector.
@(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 个评论
Stephen23
2021-12-27
Actually the error message clearly states that RHSBURGERS does not return a column vector.
The ODE45 documentation states that the objective function must return a column vector. Your function does not.
Solution: write your function so that it returns a column vector.
Titas Chattopadhyay
2021-12-27
Thank you for your answer. But, I have already written it into the presciribed one. Can you tell me how to resolve this issue?
采纳的回答
Walter Roberson
2021-12-27
编辑:Walter Roberson
2021-12-27
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
4 个评论
Torsten
2021-12-27
编辑:Torsten
2021-12-27
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,N,M),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,N,M)
% uhat = fft(u);
% duhat = i*eta.*uhat;
% dduhat = -(eta.^2).*uhat;
% du = ifft(duhat);
% ddu = ifft(dduhat);
% dudt = -u.*du + nu*ddu;
s=reshape(s,N,M);
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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