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-   -   lax friedrich scheme for shock tube problem. (http://www.cfd-online.com/Forums/main/94768-lax-friedrich-scheme-shock-tube-problem.html)

manukamin November 24, 2011 15:09

lax friedrich scheme for shock tube problem.
 
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Hi

I have written a matlab code for shocktube problem using the lax friedrich scheme. However there seems to be a bug in it, due to which it is not giving me the expected results for plots of density, pressure and velocity.

Can someone please help me debug it?

Here's the code:

clear all;
close all;
clc;


R=287;
%Cv=717;
gamma=1.4;
rhol=1;
Ul=0;
Pl=100000;

rhor=0.125;
Ur=0;
Pr=10000;

c=50;
delx=20/c;
delt=.0004278;
lambda=.001069;


for i=1:1:c+1
x(i)=-10+(i-1)*delx;
end

for i=1:1:c+1

if (x(i)<0)

rho(1,i)=rhol;
u(1,i)=Ul;
p(1,i)=Pl;

else
rho(1,i)=rhor;
u(1,i)=Ur;
p(1,i)=Pr;
end
end

for i=1:1:c+1

mom(1,i)=rho(1,i)*u(1,i);
%t(1,i)=p(1,i)/(rho(1,i)*R);
e(1,i)=p(1,i)/((gamma-1)*rho(1,i));
energ(1,i)=(e(1,i)+.5*u(1,i)^2);
energrho(1,i)=energ(1,i)*rho(1,i);
end

for n=2:1:30

for i=2:1:c

rho(n,i)= .5*(rho(n-1,i-1)+ rho(n-1,i+1))-.5*lambda*(u(n-1,i+1)*rho(n-1,i+1)-u(n-1,i-1)*rho(n-1,i-1));
mom(n,i)= .5*(mom(n-1,i-1)+ mom(n-1,i+1))-.5*lambda*(u(n-1,i+1)*mom(n-1,i+1)+p(n-1,i+1)-p(n-1,i-1)-u(n-1,i-1)*mom(n-1,i-1));
energrho(n,i)= .5*(energrho(n-1,i-1)+energrho(n-1,i+1))-.5*lambda*((u(n-1,i+1)*energrho(n-1,i+1)+p(n-1,i+1)*u(n-1,i+1) - u(n-1,i-1)*energrho(n-1,i-1)+p(n-1,i-1)*u(n-1,i-1)));

energ(n,i)=energrho(n,i)/rho(n,i);
u(n,i)=mom(n,i)/rho(n,i);
e(n,i)=energ(n,i)-.5*u(n,i)^2;
%t(n,i)=e(n,i)/Cv;
p(n,i)=(gamma-1)*rho(n,i)*e(n,i);

end


rho(n,1)=rho(1,1);
rho(n,c+1)=rho(1,c+1);
mom(n,1)=mom(1,1);
mom(n,c+1)=mom(1,c+1);
e(n,1)=e(1,1);
e(n,c+1)=e(1,c+1);
%t(n,1)=t(n,2);
%t(n,1)=e(n,1)/Cv;
%t(n,c+1)=t(n,c);
%t(n,c+1)=e(n,c+1)/Cv;
p(n,1)=p(1,1);
%p(n,1)=rho(n,1)*R*t(n,1);
p(n,c+1)=p(1,c+1);
%p(n,c+1)=rho(n,c+1)*R*t(n,c+1);
u(n,1)=u(1,1);
%u(n,1)=mom(n,1)/rho(n,1);
u(n,c+1)=u(1,c+1);
%u(n,c+1)=mom(n,c+1)/rho(n,c+1);

end



%t=plot(x,p(30,: ),'or');
%axis([-10 10 0 100000])


%t=plot(x,u(30,: ),'or');
%axis([-10 10 -150 450])

t=plot(x,rho(25,: ),'or');
axis([-10 10 0 1.1])










Thanks
Manu

manukamin November 25, 2011 01:15

Hi

never mind.. I fixed it.. I was not updating the value of energy at boundary points and it was hence taking default value of zero which is not correct.

alpesh_iitb November 3, 2013 03:21

Hi,
can you tell me what is lambda here?
also can you post the updated code?

hy1112006 March 22, 2016 02:02

Hi, can you upload the updated code?
Thanks so much!


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