function phi = main_advection(phi,f,u,v,runTime,tFinal) 
%
%***************************************************************************
%                  Program: Passive Advection Equation
%
%             Written by Chiu Yen Kao in matlab : July 2 2007
%             All rights researved !!!
%
%***************************************************************************
%
%  In this program, we are going to solve the 2D passive advection problem
%
%  The Equation is as following: 
% 
%           phi.t + (u*phi).x + (v*phi).y = f           (5)
%           where (u,v) and f is given
% on the rectangular domain
%           D = [0,1] x[0,1]
%
%  The BC for phi is: 
%   
%           phi(x,0,t)= 0
%
%***************************************************************************
global xmin xmax ymin ymax Mx My
global gx gy nx ny nxs nys nxe nye dx dy x y
global runTime


tol = 1.0e-5;


dtUp   = 0.5*dx;
dtLow  = 1e-8;


run = 0;
eps = 0;

%[u,v] = getVelocity(phi,eta,gx,gy,nx,ny,dx,dy,eps);
T_st = runTime;

%
% main time advance loop
%

while runTime < tFinal
   dtLim = getTimeStep(u,v,phi,tol,eps);
   dtRun = min(dtLim,dtUp);
   if dtRun < dtLow
      error('dtRun too small')
   end
   if (runTime + dtRun) >= tFinal
      dtRun = tFinal - runTime;
   end
   [phi,u,v] = advance(phi,f,u,v,T_st,dtRun);
   runTime = runTime + dtRun;
   run = run + 1;
end