# Several Floaters moving on Faraday waves

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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

% Plot the floater position

figure(1)

plot(x,y,'-o')

xlabel('x-position')

ylabel('y-position')

##### 1 Comment

the cyclist
on 10 Jan 2023

### Answers (1)

Bhavana Ravirala
on 23 Feb 2023

Edited: Bhavana Ravirala
on 24 Feb 2023

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!

##### 2 Comments

Thierry Rebetez
on 23 Feb 2023

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
on 24 Feb 2023

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

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