Hello all, please am solving naviers 2d for wind speed forecasting but am having error, Arrays have incompatible sizes for this operation. Error in navierstokes (line 31)

EDIT: Rearranging your code and changing format so that it can be run here.

%callup code
clear
clc
% Define test problem parameters
Lx = 1000; % Length of domain in x direction (m)
Ly = 1000; % Length of domain in y direction (m)
Nx = 100; % Number of grid points in x direction
Ny = 100; % Number of grid points in y direction
dt = 1; % Time step size (s)
t_final = 3600; % Final simulation time (s)
nu = 0.1; % Kinematic viscosity (m^2/s)
rho = 1.2; % Density of air (kg/m^3)
alpha = 0.1; % Coefficient for advection in x direction
beta = 0.2; % Coefficient for advection in y direction
dx=2

dx = 2

dy=2

dy = 2

u = zeros(Ny, Nx); % Initial u velocity field
v = zeros(Ny, Nx); % Initial v velocity field

% Define test boundary condition functions % Zero velocity at all boundaries bc_func = @(x,y,t) [0, 0, 0, 0];
% Define test wind speed profile function wind_profile_func = @(x,y,t) 10 + 2*cos(2*pi*x/Lx)*sin(2*pi*y/Ly);
% Run simulation %[u, v, x, y, t] = windSpeedForecast(Lx, Ly, Nx, Ny, dt, t_final, nu, rho, alpha
[unew,vnew]=navierstokes(u,v,dx,dy,nu,alpha,beta,dt, 100)

Unrecognized function or variable 'u_star'.

Error in solution>navierstokes (line 29)
u_new = u_star + Dx*(u_star(:,3:end)-2*u_star(:,2:end-1)+u_star(:,1:end-2)) ...

function [u,v] = navierstokes(u,v,dx,dy,nu,alpha,beta,dt,n_iterations) % Function to forecast wind speed using simplified Navier-Stokes equation % Inputs: % - u: initial x-velocity field (2D array) % - v: initial y-velocity field (2D array) % - dx: x-direction grid spacing (scalar) % - dy: y-direction grid spacing (scalar) % - nu: kinematic viscosity coefficient (scalar) % - alpha: coefficient for advection in x-direction (scalar) % - beta: coefficient for advection in y-direction (scalar) % - dt: time step size (scalar) % - n_iterations: number of iterations to perform (integer) % Outputs: % - u: final x-velocity field (2D array) % - v: final y-velocity field (2D array)
% Calculate constants N = size(u); Nx = 100; Ny = 100; ax = alpha*dt/dx; ay = alpha*dt/dy; bx = beta*dt/dx; by = beta*dt/dy; Dx = nu*dt/dx^2; Dy = nu*dt/dy^2;
% Loop over time steps for n = 1:n_iterations % Calculate intermediate velocities u_star = u + ax*(u(:,2:end)-u(:,1:end-1)) ... + by*(u(2:end,:)-u(1:end-1,:)); v_star = v + ay*(v(:,2:end)-v(:,1:end-1)) ... + bx*(v(2:end,:)-v(1:end-1,:));
% Calculate final velocities
u_new = u_star + Dx*(u_star(:,3:end)-2*u_star(:,2:end-1)+u_star(:,1:end-2)) ...
             + Dy*(u_star(3:end,:)-2*u_star(2:end-1,:)+u_star(1:end-2,:));
v_new = v_star + Dx*(v_star(:,3:end)-2*v_star(:,2:end-1)+v_star(:,1:end-2)) ...
             + Dy*(v_star(3:end,:)-2*v_star(2:end-1,:)+v_star(1:end-2,:));

% Update velocities for next time step
u = u_new;
v = v_new;
end

Answer 1

[Cris LaPierre]

This error can occur when you try to subtract two arrays of differing size.

[1 2] - [1 2 3]

Arrays have incompatible sizes for this operation.