evaluation a drag over a pre-designed model of a car using CFD

numerical solution a t=0.4seconds for different values of dt

dt is the interval between the time step. Has the value of dt becomes smaller the accuracy increases and error decreses. For dt = 1e-1 the product (c*dt/dx) is greater than 1 and the solution is blowing up.

clear all
close all
clc

%defining all the constant values       
L = 1;  
n = 81;
c = 1;


%calculation 
x = linspace(0,L,n);
dx = L/(n-1);

x_start = find(x==0.1); 
x_stop = find(x==0.3);

%initialize arrays and apply boundary conditions 
u = ones(1,n);
%u(1) = 1;
u(x_start:x_stop) = 2;
uold = u;
u_initial = u;
nt = 40;
%time loop 
for k = 1:nt
    %space loop
    dt = 1e-4;
    for i=2:n
       u(i)=uold(i)-(((c*dt)/dx)*(uold(i)-uold(i-1)));
    end
    uold = u;
end
    subplot(1,4,1)
    plot(x,u_initial,\'b\');
    hold on 
    plot(x,u,\'r\');
    title(\'For dt=1e-4\');

for k = 1:nt
    %space loop
    dt = 1e-3;
    for i=2:n
       u(i)=uold(i)-(((c*dt)/dx)*(uold(i)-uold(i-1)));
    end
    uold = u;
end
    subplot(1,4,2)
    plot(x,u_initial,\'b\');
    hold on 
    plot(x,u,\'r\');
    title(\'For dt=1e-3\');

for k = 1:nt
    %space loop
    dt = 1e-2;
    for i=2:n
       u(i)=uold(i)-(((c*dt)/dx)*(uold(i)-uold(i-1)));
    end
    uold = u;
end 
    subplot(1,4,3)
    plot(x,u_initial,\'b\');
    hold on 
    plot(x,u,\'r\');
    title(\'For dt=1e-2\');

for k = 1:nt
    %space loop
    dt = 1e-1;
    for i=2:n
       u(i)=uold(i)-(((c*dt)/dx)*(uold(i)-uold(i-1)));
    end
    uold = u;
end
    subplot(1,4,4)
    plot(x,u_initial,\'b\');
    hold on 
    plot(x,u,\'r\');
    title(\'For dt=1e-1\');