tracer test example added

Examples/Tutorial/tracer_hetrogeneous.m

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+% see http://fvt.simulkade.com/posts/2015-05-11-tracer-flow-porous-media.html
+Nx=50;
+Ny=50;
+Lx=1.0; % (m)
+Ly=1.0; % (m)
+% physical values
+D_val=1.0e-9; % (m^2/s)
+mu_val=1e-3; % (Pa.s)
+poros=0.2;
+perm_val=1.0e-12; % (m^2)
+clx=0.05;
+cly=0.05;
+V_dp=0.6;
+perm= field2d(Nx,Ny,perm_val,V_dp,clx,cly);
+% physical system
+u_inj=1.0/(3600*24); % (m/s)
+c_init=0.0;
+c_inj=1.0;
+p_out=100e5; % (Pa)
+% create mesh and assign values to the domain
+m= createMesh2D(Nx, Ny, Lx, Ly);
+k=createCellVariable(m, perm);
+phi=createCellVariable(m,poros);
+D=createCellVariable(m, D_val);
+% Define the boundaries
+BCp = createBC(m); % Neumann BC for pressure
+BCc = createBC(m); % Neumann BC for concentration
+% change the right boandary to constant pressure (Dirichlet)
+BCp.right.a(:)=0.0;
+BCp.right.b(:)=1.0;
+BCp.right.c(:)=p_out;
+% left boundary
+BCp.left.a(:)=-perm_val/mu_val;
+BCp.left.c(:)=u_inj;
+% change the left boundary to constant concentration (Dirichlet)
+BCc.left.a(:)=0.0;
+BCc.left.b(:)=1.0;
+BCc.left.c(:)=1.0;
+labda_face=harmonicMean(m, k/mu_val);
+Mdiffp=diffusionTerm(m,labda_face);
+[Mbcp, RHSp] = boundaryCondition(m,BCp);
+Mp= Mdiffp+Mbcp;
+p_val=solvePDE(m, Mp, RHSp);
+figure(1)
+visualizeCells(m,p_val);
+title('Pressure profile (Pa)');
+colorbar();
+
+% estimate a practical time step
+n_loop=50;
+dt=Lx/u_inj/(5*100); % (s)
+% find the velocity vector
+u=-labda_face.*gradientTerm(m, p_val); % (m/s)
+% find the matrices of coefficients
+D_face=harmonicMean(m, phi.*D);
+Mdiffc=diffusionTerm(m, D_face);
+Mconvc=convectionUpwindTerm(m, u);
+[Mbcc, RHSbcc] = boundaryCondition(m, BCc);
+% initialize
+c_old = createCellVariable(m, c_init, BCc);
+c.value = c_old;
+c.Old = c_old;
+% start the loop
+for i=1:n_loop
+    [Mtransc, RHStransc] = transientTerm(m, phi, dt, c);
+    Mc=-Mdiffc+Mconvc+Mbcc+Mtransc;
+    RHSc=RHSbcc+RHStransc;
+    c_val=solvePDE(m, Mc, RHSc);
+    c.Old=c_val;
+end
+figure(2);
+subplot(1,2,1);
+visualizeCells(m, c_val);
+title('concentration profile');
+colorbar();
+subplot(1,2,2);
+pcolor(k);
+colorbar()
+title('perm field');