How to stop particles crossing the solid cylinder boundary? - matlab

Question

I am doing a random walk particle tracking simulation. In my problem, I have to implement a reflected boundary on the cylinder. In this code, the check implies that if particles enter into the cylinder, their previous position should not change. I mean, if a particle crosses the solid boundary, such a move is rejected, and the tracer stays at its previous position during the current iteration. For clarification, I have attached an image where you can see particle sitting in the circle.
However, particles still entering into the cylinder. Below is my code.
%% loop starts
for i = 1:T % T is the total computation time of simulation
t = i*dt; % dt is the time step
%% Particle tracking starts
x_ out = x_previous + u.dt + sqrt(2Ddt); % x_out--> current position
% x_previous--> previous position
% u -> x-velocity component
y_ out = y_previous + v.dt + sqrt(2Ddt); % y_out--> current position
% y_previous--> previous position
% v -> y-velocity component
%% Check whether particle is inside the cylinder obstacle
% x_c and y_c is the center location for cylinder (obstacle) in the flow
Incircle = sqrt((x_out - x_c).^2 + (y_out - y_c).^2);
Particle_enter = find (Incircle < D/2); % Particle entered in obstacle
% having diameter (D)
%% if particle cross cylinder boundary, do not update its position
if ismember(Particle_enter,1)
kk1 = find(ismember(isIncircle, 1) == 1);
x_out(kk1) = x_previous(kk1); % Do not update location
y_out(kk1) = y_previous(kk1);
end
x_previous = x_out;
y_previous = y_out;
end
Any modification/correction will be helpful
Thanks

Answer 1

Due to rounding error, when comparing float or double, use
a-b > tol % tol = some error tolerance, say, 1e-10
instead of
a > b
Also, sqrt can introduce some numerical error, comparing the squared distance is more accurate.
Try to change these lines in your code into
Incircle = (x_out - x_c).^2 + (y_out - y_c).^2;
Particle_enter = find (abs(Incircle - D^2/4) < tol);
If you randomly generate the initial positions of the particles, make sure they are not inside the obstacle in the first place.
Finally, if a particle hits a reflected boundary, shouldn't it be reflected, instead of returning to where it was?