I get the error of "Array indices must be positive integers or logical values"

Iam trying to run this code but i am getting this following error "Array indices must be positive integers or logical values", how can i fix it?

My code

clc; clear all;close all;

% Define the geometry and flow conditions for the nozzle

Tt = 3000; % total temperature in the combustion chamber, in Kelvins

pt = 1500e3; % total pressure in the combustion chamber, in pascals

m = 10; % mass flow rate through the nozzle, in kilograms/second

gamma = 1.4; % ratio of specific heats for the gas

cp = 1000; % specific heat capacity at constant pressure, in joules/kilogram-kelvin

% Define the grid for the nozzle

x_min = 0.0; % minimum x coordinate of the grid, in meters

x_max = 1.0; % maximum x coordinate of the grid, in meters

nx = 100; % number of grid points in the x direction

dx = (x_max - x_min) / nx; % grid spacing in the x direction, in meters

% Initialize the flow field

u = zeros(nx, 1); % x-component of velocity, in meters/second

p = zeros(nx, 1); % pressure, in pascals

rho = zeros(nx, 1); % density, in kilograms/meter^3

T = zeros(nx, 1); % temperature, in Kelvins

% Set the inlet boundary conditions

p(1) = pt;

T(1) = Tt;

% Iterate over the characteristics to solve for the flow field

for i = 1:nx

% Compute the x-component of the characteristic direction

char_x = u(i) * rho(i);

% Compute the flow properties at the next point along the characteristic

u(i+1) = u(i) - (dx / char_x) * (p(i) - p(i-1));

rho(i+1) = rho(i) * (u(i) / u(i+1));

T(i+1) = T(i) * (rho(i) / rho(i+1))^(gamma-1);

% Compute the pressure at the next point along the characteristic

p(i+1) = p(i) + rho(i) * (u(i) - u(i+1)) * dx;

end

% Compute the flow properties at the exit of the nozzle

exit_velocity = u(nx);

exit_density = rho(nx);

exit_pressure = p(nx);

exit_temperature = T(nx);

% Print the results to the console

fprintf('Exit velocity: %f m/s\n', exit_velocity);

fprintf('Exit density: %f kg/m^3\n', exit_density);

fprintf('Exit pressure: %f Pa\n', exit_pressure);

fprintf('Exit temperature: %f K\n', exit_temperature);

% Compute the Mach number at each point in the nozzle

Mach = u ./ sqrt(gamma * cp * T);

% Plot the flow properties as contour plots

figure;

subplot(2,2,1);

contourf(Mach);

xlabel('x (m)');

ylabel('y (m)');

title('Mach number');

subplot(2,2,2);

contourf(p/1e3);

xlabel('x (m)');

ylabel('y (m)');

title('Pressure (kPa)');

subplot(2,2,3);

contourf(T); % Plot the flow properties as contour plots

figure;

subplot(2,2,1);

contourf(Mach);

xlabel('x (m)');

ylabel('y (m)');

title('Mach number');

subplot(2,2,2);

contourf(p/1e3);

xlabel('x (m)');

ylabel('y (m)');

title('Pressure (kPa)');

subplot(2,2,3);

contourf(T);

xlabel('x (m)');

ylabel('y (m)');

title('Temperature (K)');

subplot(2,2,4);

contourf(rho);

xlabel('x (m)');

ylabel('y (m)');

title('Density (kg/m^3)');

% Plot the velocity magnitude as a line plot

figure;

plot(sqrt(u.^2 + v.^2));

xlabel('x (m)');

ylabel('Velocity magnitude (m/s)');

title('Velocity magnitude');

Answer 1

[Sulaymon Eshkabilov]

Make these corrections in your code's loop iteration:

...
    for i = 2:nx
    % Compute the x-component of the characteristic direction
    char_x = u(i-1) * rho(i-1);
    
% Compute the flow properties at the next point along the characteristic
    u(i) = u(i-1) - (dx / char_x) * (p(i) - p(i-1));
    rho(i) = rho(i-1) * (u(i-1) / u(i));
    T(i) = T(i-1) * (rho(i-1) / rho(i))^(gamma-1);
    % Compute the pressure at the next point along the characteristic
    p(i) = p(i-1) + rho(i-1) * (u(i-1) - u(i)) * dx;
end

[Mohamed T. Adam]

thank you so much

[Sulaymon Eshkabilov]

Most welcome!

Answer 2

[Image Analyst]

Did you search for the error? We get asked this several times per week so you would have found it. It's a FAQ:

https://matlab.fandom.com/wiki/FAQ#%22Subscript_indices_must_either_be_real_positive_integers_or_logicals.%22