Fluid Pathline using Euler's Method with MATLAB

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1 个投票

Hello.

I'm trying solve a problem of my course lecture in Fluid Mechanics.

We have velocity: u = y^2 - x^2 + t^2 at X-direction and v= 2xy + 20t at Y-direction.

To find the pathline of fluid we have the initial conditions that x0=1.5, y0=1 and t0=0 and we should use Euler's Method to determine the function.

I use the step of 0.001 for the time variable until t(final) = 10.

The problem in below program is debugging. Can someone help me ?

clear all
clc
f=@(x,y,t)y^2-x*2+t^2; 
g=@(x,y,t)2*x*y + 20*t;
x0=input('\n Enter initial value of x i.e. x0: '); 
y0=input('\n Enter initial value of y i.e. y0: '); 
t0=input('\n Enter initial value of t i.e. t0: '); 
tn=input('\n Enter the final value of t: ');
h=input('\n Enter the step length h: '); %example h=0.001
 %Formula: y1=y0+h*function(x0,y0,t0);
 fprintf('\n t        x         y');
while t0<=tn
    fprintf('\n%4.3f  %4.3f  %4.3g',t0,x0,y0); %values of t and x and y 
    x1=x0+h*f(x0,y0,t0);
    y1=y0+h*g(x0,y0,t0);
    t1=t0+h;
    x0=x1;
    y0=y1;  
end