Using subs To Solve sims Equation with Points on A Grid
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Hi,
I'm trying to use subs to subsitute x and y coordinates into a symbolic equation so I can solve it for the value at each coordinate. Below is how my code is currently sctructured.
%% Creating Fluid Equations
syms x y
vel_x = sin(x) + cos(y);
vel_y = cos(x)^2 + sin(y)^0.5;
pressure = 101300 * (x*exp(y));
density = 1.2 * (x^2 + y^0.5);
%% Plotting Fluid Equations
x_input = 0:0.1:10;
y_input = 0:0.1:10;
[x_coord, y_coord] = meshgrid(x_input, y_input);
% Subsitute symbolic variables with x and y arrays and turn into array of
% doubles
vel_x = double(subs(vel_x, [x, y], {x_coord, y_coord}));
vel_y = double(subs(vel_y, [x, y], {x_coord, y_coord}));
pressure = double(subs(pressure, [x, y], {x_coord, y_coord}));
density = double(subs(density, [x, y], {x_coord, y_coord}));
surf(x_input, y_input, vel_x)
This code is already taking 5 whole seconds to run and ideally I'd like to increase the density of coordinates. I was trying to stay away from using for loops wich is how I ended up using meshgrid and subs instead. How can I make this much more efficient?
Any advice would be much appreciated thank you!
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