Why does the pressure diverge so quickly, and what is the solution?
clc; % Clear the command window
clear; % Clear all variables
% Input parameters
rho_fluid = 1220;
rho_copper = 8960; % Density of copper in kg/m^3
L_X = 0.0043;
L_Y = 0.0001;
L_Z = 0.0002;
n_X = 300;
n_Y = 50;
n_Z = 50;
u_inlet = 0.05; % Reduced inlet velocity in m/s
nu = 1e-6; % Kinematic viscosity of the fluid (m^2/s)
tolerance = 1e-6; % Convergence tolerance
max_iter = 10000; % Maximum number of iterations
dt = 1e-10; % Further reduced time step for better numerical stability
% Calculate delta
delta_x = L_X / (n_X – 1); % Grid spacing in X direction
delta_y = L_Y / (n_Y – 1); % Grid spacing in Y direction
delta_z = L_Z / (n_Z – 1); % Grid spacing in Z direction
% Define pin positions and dimensions
pin_radius = 0.0001; % Radius of the pins
pin_height = L_Z; % Height of the pins (same as channel height)
pin_positions = [0.001 0.00005; 0.002 0.00005; 0.003 0.00005; 0.0015 0.00005; 0.0025 0.00005]; % X and Y coordinates of pin centers
% Identify grid points inside and on the surface of pins
is_pin = false(n_X, n_Y, n_Z);
is_surface_pin = false(n_X, n_Y, n_Z);
for p = 1:size(pin_positions, 1)
for i = 1:n_X
for j = 1:n_Y
for k = 1:n_Z
x = (i-1) * delta_x;
y = (j-1) * delta_y;
distance = sqrt((x – pin_positions(p, 1))^2 + (y – pin_positions(p, 2))^2);
if distance <= pin_radius
is_pin(i, j, k) = true;
end
if abs(distance – pin_radius) < (delta_x / 2) % Near the surface
is_surface_pin(i, j, k) = true;
end
end
end
end
end
% Initialize velocity and pressure fields
u = zeros(n_X, n_Y, n_Z); % Initialize with zeros to avoid initial instability
v = zeros(n_X, n_Y, n_Z);
w = zeros(n_X, n_Y, n_Z);
p = zeros(n_X, n_Y, n_Z);
% Time-stepping method for solving Navier-Stokes equations using ADI method
for iter = 1:max_iter
u_old = u;
v_old = v;
w_old = w;
p_old = p;
% Solve for velocity fields (x-direction)
for j = 2:n_Y-1
for k = 2:n_Z-1
for i = 2:n_X-1
if ~is_pin(i, j, k)
% x-momentum equation (ADI method)
u(i,j,k) = u_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (u_old(i+1,j,k) – u_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (u_old(i,j+1,k) – u_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (u_old(i,j,k+1) – u_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i+1,j,k) – p_old(i-1,j,k)) / (2 * delta_x * rho_fluid) …
+ nu * ((u_old(i+1,j,k) – 2*u_old(i,j,k) + u_old(i-1,j,k)) / delta_x^2 …
+ (u_old(i,j+1,k) – 2*u_old(i,j,k) + u_old(i,j-1,k)) / delta_y^2 …
+ (u_old(i,j,k+1) – 2*u_old(i,j,k) + u_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (y-direction)
for i = 2:n_X-1
for k = 2:n_Z-1
for j = 2:n_Y-1
if ~is_pin(i, j, k)
% y-momentum equation (ADI method)
v(i,j,k) = v_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (v_old(i+1,j,k) – v_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (v_old(i,j+1,k) – v_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (v_old(i,j,k+1) – v_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j+1,k) – p_old(i,j-1,k)) / (2 * delta_y * rho_fluid) …
+ nu * ((v_old(i+1,j,k) – 2*v_old(i,j,k) + v_old(i-1,j,k)) / delta_x^2 …
+ (v_old(i,j+1,k) – 2*v_old(i,j,k) + v_old(i,j-1,k)) / delta_y^2 …
+ (v_old(i,j,k+1) – 2*v_old(i,j,k) + v_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (z-direction)
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
% z-momentum equation (ADI method)
w(i,j,k) = w_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (w_old(i+1,j,k) – w_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (w_old(i,j+1,k) – w_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (w_old(i,j,k+1) – w_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j,k+1) – p_old(i,j,k-1)) / (2 * delta_z * rho_fluid) …
+ nu * ((w_old(i+1,j,k) – 2*w_old(i,j,k) + w_old(i-1,j,k)) / delta_x^2 …
+ (w_old(i,j+1,k) – 2*w_old(i,j,k) + w_old(i,j-1,k)) / delta_y^2 …
+ (w_old(i,j,k+1) – 2*w_old(i,j,k) + w_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for pressure field using the pressure Poisson equation
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
p(i,j,k) = (p_old(i+1,j,k) + p_old(i-1,j,k) + p_old(i,j+1,k) + p_old(i,j-1,k) + p_old(i,j,k+1) + p_old(i,j,k-1)) / 6 …
– (rho_fluid / 6) * ((u(i+1,j,k) – u(i-1,j,k)) / (2 * delta_x) …
+ (v(i,j+1,k) – v(i,j-1,k)) / (2 * delta_y) …
+ (w(i,j,k+1) – w(i,j,k-1)) / (2 * delta_z));
end
end
end
end
% Inlet boundary condition for velocity
u(1, :, π = u_inlet;
% Outlet boundary condition for pressure
p(n_X, :, π = 0; % Assume atmospheric pressure at the outlet
% No-slip boundary conditions for velocity at the walls and pins
u(:, :, 1) = 0; % Bottom wall
u(:, :, n_Z) = 0; % Top wall
u(is_pin) = 0; % Surface of pins
v(:, :, 1) = 0; % Bottom wall
v(:, :, n_Z) = 0; % Top wall
v(is_pin) = 0; % Surface of pins
w(:, :, 1) = 0; % Bottom wall
w(:, :, n_Z) = 0; % Top wall
w(is_pin) = 0; % Surface of pins
% Symmetry boundary conditions for velocity at the side walls
u(:, 1, π = u(:, 2, :); % Left side wall
u(:, n_Y, π = u(:, n_Y-1, :); % Right side wall
v(:, 1, π = v(:, 2, :); % Left side wall
v(:, n_Y, π = v(:, n_Y-1, :); % Right side wall
w(:, 1, π = w(:, 2, :); % Left side wall
w(:, n_Y, π = w(:, n_Y-1, :); % Right side wall
% Convergence check
max_diff_u = max(max(max(abs(u – u_old))));
max_diff_v = max(max(max(abs(v – v_old))));
max_diff_w = max(max(max(abs(w – w_old))));
max_diff_p = max(max(max(abs(p – p_old))));
disp([‘Max difference in u: ‘, num2str(max_diff_u)]);
disp([‘Max difference in v: ‘, num2str(max_diff_v)]);
disp([‘Max difference in w: ‘, num2str(max_diff_w)]);
disp([‘Max difference in p: ‘, num2str(max_diff_p)]);
if max_diff_u < tolerance && max_diff_v < tolerance && max_diff_w < tolerance && max_diff_p < tolerance
disp(‘Converged’);
break; % Exit the loop if converged
end
% Check for NaN or Inf values
if any(isnan(u(:))) || any(isinf(u(:))) || any(isnan(v(:))) || any(isinf(v(:))) || any(isnan(w(:))) || any(isinf(w(:))) || any(isnan(p(:))) || any(isinf(p(:)))
disp(‘Error: NaN or Inf detected in velocity or pressure matrix’);
break;
end
endclc; % Clear the command window
clear; % Clear all variables
% Input parameters
rho_fluid = 1220;
rho_copper = 8960; % Density of copper in kg/m^3
L_X = 0.0043;
L_Y = 0.0001;
L_Z = 0.0002;
n_X = 300;
n_Y = 50;
n_Z = 50;
u_inlet = 0.05; % Reduced inlet velocity in m/s
nu = 1e-6; % Kinematic viscosity of the fluid (m^2/s)
tolerance = 1e-6; % Convergence tolerance
max_iter = 10000; % Maximum number of iterations
dt = 1e-10; % Further reduced time step for better numerical stability
% Calculate delta
delta_x = L_X / (n_X – 1); % Grid spacing in X direction
delta_y = L_Y / (n_Y – 1); % Grid spacing in Y direction
delta_z = L_Z / (n_Z – 1); % Grid spacing in Z direction
% Define pin positions and dimensions
pin_radius = 0.0001; % Radius of the pins
pin_height = L_Z; % Height of the pins (same as channel height)
pin_positions = [0.001 0.00005; 0.002 0.00005; 0.003 0.00005; 0.0015 0.00005; 0.0025 0.00005]; % X and Y coordinates of pin centers
% Identify grid points inside and on the surface of pins
is_pin = false(n_X, n_Y, n_Z);
is_surface_pin = false(n_X, n_Y, n_Z);
for p = 1:size(pin_positions, 1)
for i = 1:n_X
for j = 1:n_Y
for k = 1:n_Z
x = (i-1) * delta_x;
y = (j-1) * delta_y;
distance = sqrt((x – pin_positions(p, 1))^2 + (y – pin_positions(p, 2))^2);
if distance <= pin_radius
is_pin(i, j, k) = true;
end
if abs(distance – pin_radius) < (delta_x / 2) % Near the surface
is_surface_pin(i, j, k) = true;
end
end
end
end
end
% Initialize velocity and pressure fields
u = zeros(n_X, n_Y, n_Z); % Initialize with zeros to avoid initial instability
v = zeros(n_X, n_Y, n_Z);
w = zeros(n_X, n_Y, n_Z);
p = zeros(n_X, n_Y, n_Z);
% Time-stepping method for solving Navier-Stokes equations using ADI method
for iter = 1:max_iter
u_old = u;
v_old = v;
w_old = w;
p_old = p;
% Solve for velocity fields (x-direction)
for j = 2:n_Y-1
for k = 2:n_Z-1
for i = 2:n_X-1
if ~is_pin(i, j, k)
% x-momentum equation (ADI method)
u(i,j,k) = u_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (u_old(i+1,j,k) – u_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (u_old(i,j+1,k) – u_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (u_old(i,j,k+1) – u_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i+1,j,k) – p_old(i-1,j,k)) / (2 * delta_x * rho_fluid) …
+ nu * ((u_old(i+1,j,k) – 2*u_old(i,j,k) + u_old(i-1,j,k)) / delta_x^2 …
+ (u_old(i,j+1,k) – 2*u_old(i,j,k) + u_old(i,j-1,k)) / delta_y^2 …
+ (u_old(i,j,k+1) – 2*u_old(i,j,k) + u_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (y-direction)
for i = 2:n_X-1
for k = 2:n_Z-1
for j = 2:n_Y-1
if ~is_pin(i, j, k)
% y-momentum equation (ADI method)
v(i,j,k) = v_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (v_old(i+1,j,k) – v_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (v_old(i,j+1,k) – v_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (v_old(i,j,k+1) – v_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j+1,k) – p_old(i,j-1,k)) / (2 * delta_y * rho_fluid) …
+ nu * ((v_old(i+1,j,k) – 2*v_old(i,j,k) + v_old(i-1,j,k)) / delta_x^2 …
+ (v_old(i,j+1,k) – 2*v_old(i,j,k) + v_old(i,j-1,k)) / delta_y^2 …
+ (v_old(i,j,k+1) – 2*v_old(i,j,k) + v_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (z-direction)
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
% z-momentum equation (ADI method)
w(i,j,k) = w_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (w_old(i+1,j,k) – w_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (w_old(i,j+1,k) – w_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (w_old(i,j,k+1) – w_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j,k+1) – p_old(i,j,k-1)) / (2 * delta_z * rho_fluid) …
+ nu * ((w_old(i+1,j,k) – 2*w_old(i,j,k) + w_old(i-1,j,k)) / delta_x^2 …
+ (w_old(i,j+1,k) – 2*w_old(i,j,k) + w_old(i,j-1,k)) / delta_y^2 …
+ (w_old(i,j,k+1) – 2*w_old(i,j,k) + w_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for pressure field using the pressure Poisson equation
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
p(i,j,k) = (p_old(i+1,j,k) + p_old(i-1,j,k) + p_old(i,j+1,k) + p_old(i,j-1,k) + p_old(i,j,k+1) + p_old(i,j,k-1)) / 6 …
– (rho_fluid / 6) * ((u(i+1,j,k) – u(i-1,j,k)) / (2 * delta_x) …
+ (v(i,j+1,k) – v(i,j-1,k)) / (2 * delta_y) …
+ (w(i,j,k+1) – w(i,j,k-1)) / (2 * delta_z));
end
end
end
end
% Inlet boundary condition for velocity
u(1, :, π = u_inlet;
% Outlet boundary condition for pressure
p(n_X, :, π = 0; % Assume atmospheric pressure at the outlet
% No-slip boundary conditions for velocity at the walls and pins
u(:, :, 1) = 0; % Bottom wall
u(:, :, n_Z) = 0; % Top wall
u(is_pin) = 0; % Surface of pins
v(:, :, 1) = 0; % Bottom wall
v(:, :, n_Z) = 0; % Top wall
v(is_pin) = 0; % Surface of pins
w(:, :, 1) = 0; % Bottom wall
w(:, :, n_Z) = 0; % Top wall
w(is_pin) = 0; % Surface of pins
% Symmetry boundary conditions for velocity at the side walls
u(:, 1, π = u(:, 2, :); % Left side wall
u(:, n_Y, π = u(:, n_Y-1, :); % Right side wall
v(:, 1, π = v(:, 2, :); % Left side wall
v(:, n_Y, π = v(:, n_Y-1, :); % Right side wall
w(:, 1, π = w(:, 2, :); % Left side wall
w(:, n_Y, π = w(:, n_Y-1, :); % Right side wall
% Convergence check
max_diff_u = max(max(max(abs(u – u_old))));
max_diff_v = max(max(max(abs(v – v_old))));
max_diff_w = max(max(max(abs(w – w_old))));
max_diff_p = max(max(max(abs(p – p_old))));
disp([‘Max difference in u: ‘, num2str(max_diff_u)]);
disp([‘Max difference in v: ‘, num2str(max_diff_v)]);
disp([‘Max difference in w: ‘, num2str(max_diff_w)]);
disp([‘Max difference in p: ‘, num2str(max_diff_p)]);
if max_diff_u < tolerance && max_diff_v < tolerance && max_diff_w < tolerance && max_diff_p < tolerance
disp(‘Converged’);
break; % Exit the loop if converged
end
% Check for NaN or Inf values
if any(isnan(u(:))) || any(isinf(u(:))) || any(isnan(v(:))) || any(isinf(v(:))) || any(isnan(w(:))) || any(isinf(w(:))) || any(isnan(p(:))) || any(isinf(p(:)))
disp(‘Error: NaN or Inf detected in velocity or pressure matrix’);
break;
end
endΒ clc; % Clear the command window
clear; % Clear all variables
% Input parameters
rho_fluid = 1220;
rho_copper = 8960; % Density of copper in kg/m^3
L_X = 0.0043;
L_Y = 0.0001;
L_Z = 0.0002;
n_X = 300;
n_Y = 50;
n_Z = 50;
u_inlet = 0.05; % Reduced inlet velocity in m/s
nu = 1e-6; % Kinematic viscosity of the fluid (m^2/s)
tolerance = 1e-6; % Convergence tolerance
max_iter = 10000; % Maximum number of iterations
dt = 1e-10; % Further reduced time step for better numerical stability
% Calculate delta
delta_x = L_X / (n_X – 1); % Grid spacing in X direction
delta_y = L_Y / (n_Y – 1); % Grid spacing in Y direction
delta_z = L_Z / (n_Z – 1); % Grid spacing in Z direction
% Define pin positions and dimensions
pin_radius = 0.0001; % Radius of the pins
pin_height = L_Z; % Height of the pins (same as channel height)
pin_positions = [0.001 0.00005; 0.002 0.00005; 0.003 0.00005; 0.0015 0.00005; 0.0025 0.00005]; % X and Y coordinates of pin centers
% Identify grid points inside and on the surface of pins
is_pin = false(n_X, n_Y, n_Z);
is_surface_pin = false(n_X, n_Y, n_Z);
for p = 1:size(pin_positions, 1)
for i = 1:n_X
for j = 1:n_Y
for k = 1:n_Z
x = (i-1) * delta_x;
y = (j-1) * delta_y;
distance = sqrt((x – pin_positions(p, 1))^2 + (y – pin_positions(p, 2))^2);
if distance <= pin_radius
is_pin(i, j, k) = true;
end
if abs(distance – pin_radius) < (delta_x / 2) % Near the surface
is_surface_pin(i, j, k) = true;
end
end
end
end
end
% Initialize velocity and pressure fields
u = zeros(n_X, n_Y, n_Z); % Initialize with zeros to avoid initial instability
v = zeros(n_X, n_Y, n_Z);
w = zeros(n_X, n_Y, n_Z);
p = zeros(n_X, n_Y, n_Z);
% Time-stepping method for solving Navier-Stokes equations using ADI method
for iter = 1:max_iter
u_old = u;
v_old = v;
w_old = w;
p_old = p;
% Solve for velocity fields (x-direction)
for j = 2:n_Y-1
for k = 2:n_Z-1
for i = 2:n_X-1
if ~is_pin(i, j, k)
% x-momentum equation (ADI method)
u(i,j,k) = u_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (u_old(i+1,j,k) – u_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (u_old(i,j+1,k) – u_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (u_old(i,j,k+1) – u_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i+1,j,k) – p_old(i-1,j,k)) / (2 * delta_x * rho_fluid) …
+ nu * ((u_old(i+1,j,k) – 2*u_old(i,j,k) + u_old(i-1,j,k)) / delta_x^2 …
+ (u_old(i,j+1,k) – 2*u_old(i,j,k) + u_old(i,j-1,k)) / delta_y^2 …
+ (u_old(i,j,k+1) – 2*u_old(i,j,k) + u_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (y-direction)
for i = 2:n_X-1
for k = 2:n_Z-1
for j = 2:n_Y-1
if ~is_pin(i, j, k)
% y-momentum equation (ADI method)
v(i,j,k) = v_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (v_old(i+1,j,k) – v_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (v_old(i,j+1,k) – v_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (v_old(i,j,k+1) – v_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j+1,k) – p_old(i,j-1,k)) / (2 * delta_y * rho_fluid) …
+ nu * ((v_old(i+1,j,k) – 2*v_old(i,j,k) + v_old(i-1,j,k)) / delta_x^2 …
+ (v_old(i,j+1,k) – 2*v_old(i,j,k) + v_old(i,j-1,k)) / delta_y^2 …
+ (v_old(i,j,k+1) – 2*v_old(i,j,k) + v_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for velocity fields (z-direction)
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
% z-momentum equation (ADI method)
w(i,j,k) = w_old(i,j,k) + dt/2 * ( …
– u_old(i,j,k) * (w_old(i+1,j,k) – w_old(i-1,j,k)) / (2 * delta_x) …
– v_old(i,j,k) * (w_old(i,j+1,k) – w_old(i,j-1,k)) / (2 * delta_y) …
– w_old(i,j,k) * (w_old(i,j,k+1) – w_old(i,j,k-1)) / (2 * delta_z) …
+ (p_old(i,j,k+1) – p_old(i,j,k-1)) / (2 * delta_z * rho_fluid) …
+ nu * ((w_old(i+1,j,k) – 2*w_old(i,j,k) + w_old(i-1,j,k)) / delta_x^2 …
+ (w_old(i,j+1,k) – 2*w_old(i,j,k) + w_old(i,j-1,k)) / delta_y^2 …
+ (w_old(i,j,k+1) – 2*w_old(i,j,k) + w_old(i,j,k-1)) / delta_z^2) …
);
end
end
end
end
% Solve for pressure field using the pressure Poisson equation
for i = 2:n_X-1
for j = 2:n_Y-1
for k = 2:n_Z-1
if ~is_pin(i, j, k)
p(i,j,k) = (p_old(i+1,j,k) + p_old(i-1,j,k) + p_old(i,j+1,k) + p_old(i,j-1,k) + p_old(i,j,k+1) + p_old(i,j,k-1)) / 6 …
– (rho_fluid / 6) * ((u(i+1,j,k) – u(i-1,j,k)) / (2 * delta_x) …
+ (v(i,j+1,k) – v(i,j-1,k)) / (2 * delta_y) …
+ (w(i,j,k+1) – w(i,j,k-1)) / (2 * delta_z));
end
end
end
end
% Inlet boundary condition for velocity
u(1, :, π = u_inlet;
% Outlet boundary condition for pressure
p(n_X, :, π = 0; % Assume atmospheric pressure at the outlet
% No-slip boundary conditions for velocity at the walls and pins
u(:, :, 1) = 0; % Bottom wall
u(:, :, n_Z) = 0; % Top wall
u(is_pin) = 0; % Surface of pins
v(:, :, 1) = 0; % Bottom wall
v(:, :, n_Z) = 0; % Top wall
v(is_pin) = 0; % Surface of pins
w(:, :, 1) = 0; % Bottom wall
w(:, :, n_Z) = 0; % Top wall
w(is_pin) = 0; % Surface of pins
% Symmetry boundary conditions for velocity at the side walls
u(:, 1, π = u(:, 2, :); % Left side wall
u(:, n_Y, π = u(:, n_Y-1, :); % Right side wall
v(:, 1, π = v(:, 2, :); % Left side wall
v(:, n_Y, π = v(:, n_Y-1, :); % Right side wall
w(:, 1, π = w(:, 2, :); % Left side wall
w(:, n_Y, π = w(:, n_Y-1, :); % Right side wall
% Convergence check
max_diff_u = max(max(max(abs(u – u_old))));
max_diff_v = max(max(max(abs(v – v_old))));
max_diff_w = max(max(max(abs(w – w_old))));
max_diff_p = max(max(max(abs(p – p_old))));
disp([‘Max difference in u: ‘, num2str(max_diff_u)]);
disp([‘Max difference in v: ‘, num2str(max_diff_v)]);
disp([‘Max difference in w: ‘, num2str(max_diff_w)]);
disp([‘Max difference in p: ‘, num2str(max_diff_p)]);
if max_diff_u < tolerance && max_diff_v < tolerance && max_diff_w < tolerance && max_diff_p < tolerance
disp(‘Converged’);
break; % Exit the loop if converged
end
% Check for NaN or Inf values
if any(isnan(u(:))) || any(isinf(u(:))) || any(isnan(v(:))) || any(isinf(v(:))) || any(isnan(w(:))) || any(isinf(w(:))) || any(isnan(p(:))) || any(isinf(p(:)))
disp(‘Error: NaN or Inf detected in velocity or pressure matrix’);
break;
end
endΒ navier-stocks divergenceΒ MATLAB Answers β New Questions
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