Several Floaters moving on Faraday waves

Why does this code not function? A big thank you to who can help me !

% Parameters
L = 1; % length of the container
w = 2*pi; % angular frequency of the driving force
d = 0.1; % depth of the container
g = 9.81; % acceleration due to gravity
rho = 1; % density of the fluid
A = 0.1; % amplitude of the driving force
% Discretization
Nx = 100; % number of points in the x direction
Ny = 100; % number of points in the y direction
dx = L/Nx; % spatial step in the x direction
dy = d/Ny; % spatial step in the y direction
x = linspace(0, L, Nx+1); % x-coordinates of the grid points
y = linspace(0, d, Ny+1); % y-coordinates of the grid points
% Time stepping
T = 10; % total simulation time
dt = 0.001; % time step
Nt = T/dt; % number of time steps
% Initialize variables
eta = zeros(Nx+1, Ny+1); % free surface elevation
h = zeros(Nx+1, Ny+1); % fluid depth
u = zeros(Nx+1, Ny+1); % x-velocity of the fluid
v = zeros(Nx+1, Ny+1); % y-velocity of the fluid
%Floater parameter
m = 1; % mass
k = 1; % spring constant
c = 0.1; % damping constant
x0 = 0.5; %initial x position
y0 = 0.5; %initial y position
% Time-stepping loop
for n = 1:Nt
    % Compute the fluid depth at the new time step
    h = eta + d;
    % Compute the x-velocity of the fluid
    u(2:end-1,2:end-1) = -g/w*(diff(eta, 1, 1)/dy + diff(h, 1, 2)/dx);
    % Compute the y-velocity of the fluid
    v(2:end-1,2:end-1) = g/w*(diff(eta, 1, 2)/dx - diff(h, 1, 1)/dy);
    % Enforce the no-normal flow boundary condition at the top
    u(:, end) = 0;
    v(:, end) = 0;
    % Compute the free surface elevation at the new time step
    eta(2:end-1,2:end-1) = eta(2:end-1,2:end-1) - dt*rho*(diff(u, 1, 1)/dy + diff(v, 1, 2)/dx);
    % Add the driving force
    eta(:, 1) = eta(:, 1) + A*sin(w*n*dt);
    
    % Floater position and velocity 
    x(n+1) = x(n) + dt*vx(n);
    y(n+1) = y(n) + dt*vy(n);
    vx(n+1) = vx(n) + (dt/m)*(-k*(x(n)-x0)-c*vx(n) + interp2(x,y,u,x(n),y(n)));
    vy(n+1) = vy(n) + (dt/m)*(-k*(y(n)-y0)-c*vy(n) + interp2(x,y,v,x(n),y(n)));
end

Arrays have incompatible sizes for this operation.

% Plot the floater position
figure(1)
plot(x,y,'-o')
xlabel('x-position')
ylabel('y-position')

[the cyclist]

I just formatted your code here, and ran it. I assume that that is the error message you got when you ran it locally?

Answer 1

[Bhavana Ravirala]

Hi Thierry,

I understand that you are getting the error ‘Arrays have incompatible sizes for this operation’ while you are running the code.

This is because while you are computing the x-velocity and y-velocity of the fluid you are trying to add two matrices of different sizes.

%u(2:end-1,2:end-1) = -g/w*(diff(eta, 1, 1)/dy + diff(h, 1, 2)/dx);
i= diff(eta, 1, 1)/dy; % is of size 100x101
j= diff(h, 1, 2)/dx; % is of size 101x100

Hope this helps!

[Thierry Rebetez]

Hi Bhavana,

Thanks a lot for your comment! I understand the issue. Do you know what I have to change in the code in order to "by pass" the issue?

Thank you!

Thierry

[Bhavana Ravirala]

Hi Thierry,

Can you share an example which shows the expected result of addition of the matrices. So I can understand the use case better.

Thanks

Bhavana