I understand that you want to plot velocity-time graph for diffusion of a fluid at a particular grid cell, in order to do that you will need to simulate the diffusion process over time and record the velocity at the grid cell of interest at each timestep. The simulation would typically involve solving a partial differential equation (PDE) like the diffusion equation, which might be done using numerical methods such as finite differences.
Here's a conceptual outline of how you might implement such a simulation in MATLAB. This example will not include the actual diffusion equation solver, which can be quite complex, but will show you how to set up the data collection for plotting:
% Define the simulation parameters
tmax = 100; % Maximum time
dt = 1; % Time step size
jmax = 100; % Number of grid cells in the j-direction
imax = 100; % Number of grid cells in the i-direction
vmax = 1; % Maximum fluid velocity
% Initialize the velocity matrix
U = zeros(jmax, imax); % Initial conditions
U(20:60, 35:50) = vmax; % Location of our fluid
% Choose the grid cell to monitor
j_cell = 40; % j-index of the cell to monitor
i_cell = 42; % i-index of the cell to monitor
% Initialize an array to store velocity at the grid cell over time
velocity_time = zeros(tmax, 1);
% Simulation loop
for t = 1:tmax
% Here you would implement your diffusion solver to update U
% For example: U = diffusionSolver(U, dt);
% (This function is not provided and would need to be implemented)
% Record the velocity at the specified grid cell
velocity_time(t) = U(j_cell, i_cell);
% Update the velocity matrix U for the next timestep
% (This would be part of your diffusion solver)
end
% Plot the velocity-time graph
plot(1:tmax, velocity_time);
xlabel('Time');
ylabel('Velocity');
title(sprintf('Velocity at grid cell (%d, %d) over time', j_cell, i_cell));
Find below the documentation of PDE toolbox which will be helpful for your implementation.
Hope this helps!
