Lax wendroff two step method, matlab programming

  • #1
hi i have been trying to program a general problem to the lax wednroff technique that when done i can hopefully expand on to model a dam break, before i move on im hoping if someone could tell me if im on the right tracks thanks kyle

function compare
close all;clc;clear all

%intial values
ntime = 1000000; dt=0.00040; nx=100; time = 0; a=1;output=0.4;
%step size calculation
dx= (1/nx);
%create size of u_int vector
u_int = zeros(nx,2);
%create little u_int vector for the initial values of height begining and
%end depending which value of A is used
u_int(nx,2) = 1;
u_int(1,1) = 1;

%loop for the two directions needed
for vec = 1:2
% %lax_wendroff
= lax_wendroff_2(nx,a,output, dt, ntime, time,u_int, vec,dx);
figure(vec)
plot(U(:,vec),'r*');grid on;legend('centered');
hold on
end
end


function = lax_wendroff_2(nx,a,output, dt, ntime, time,u_int, vec,dx);
%compute original size matracies
U=zeros(nx,1);
update = U ;
F = U;
if vec == 1;
U(1,vec)=u_int(1,vec);
A=a;
else
U(nx,vec)=u_int(nx,vec);
A=-a;
end
for p = 1:ntime;
if(time + dt>output); dt=output-time;
end
coeff=dt/dx;
%calculate interim steps
for i = 1:(nx-1)
F(i+1,vec)= ((U(i,vec)+U(i+1,vec))/2) - ((A*coeff)*((U(i+1,vec) - U(i,vec))));
end
for i = 2:(nx-1)
update(i,vec) = U(i,vec) - coeff*A*(F(i+1,vec) - F(i,vec));
end
for i = 2:(nx-1)
U(i,vec) = update(i,vec);
end
time = time + dt;
if time==output
break
end

end
end
 

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