k_f_euler.asv

% Kinetic flux for euler equation
% ul - 1x3 array, state on the left
% ur - 1x3 array, state on the right
% flux - 1x1x3 array, output flux
% Author Luo Li, lluoac@ust.hk
function [flux]=k_f_euler(ul,ur)
gammer=1.4;
pi=3.1415;
flux=zeros(1,3);

% left state
rhol=ul(1);
rhoul=ul(2);
rhoEl=ul(3);
ulx=rhoul/rhol;
pl=(gammer-1.)*(rhoEl-0.5*rhoul*rhoul/rhol);
laml=rhol/(2.*pl);
u0l=0.5*erfc(-sqrt(laml)*ulx);
u1l=ulx*u0l+0.5*exp(-laml*ulx*ulx)/sqrt(pi*laml);
u2l=ulx*u1l+0.5/laml*u0l;
u3l=ulx*u2l+1./laml*u1l;

% right state
rhor=ur(1);
rhour=ur(2);
rhoEr=ur(3);
urx=rhour/rhor;
pr=(gammer-1.)*(rhoEr-0.5*rhour*rhour/rhor);
lamr=rhor/(2.*pr);
u0r=0.5*erfc(sqrt(lamr)*urx);
u1r=urx*u0r-0.5*exp(-lamr*urx*urx)/sqrt(pi*lamr);
u2r=urx*u1r+0.5/lamr*u0r;
u3r=urx*u2r+1./lamr*u1r;

% flux
flux(1,1)=rhol*u1l*1.*1.+rhor*u1r*1.*1.;
flux(1,2)=rhol*u2l*1.*1.+rhor*u2r*1.*1.;
flux(1,3)=0.5*rhol*(u3l*1.*1.+u1l*1./(2*laml)*1.+u1l*1.*1./(2*laml))+0.5*rhor*(u3r*1.*1.+u1r*1./(2*lamr)*1.+u1r*1.*1./(2*lamr));