Generalizing script. Optimizing mesh.

ternary_frap.m

@@ -4,39 +4,50 @@
 % conditions are introduced. Integration of model via pdepe.
 
 a = -50;
-b = 0.01;
+b = 0.025;
 c = 1/100000;
-u0 = 0.3;
+u0 = 0.05;
+e = 0.4;
 %% Solve pde
-x = [linspace(49, 55, 600), linspace(55.01, 200, 300)];
-t = linspace(0, 0.001, 1000);
+x = [linspace(49.0, 51, 3000), linspace(51.01, 200, 300)];
+t = linspace(0.001, 1, 1000);
 fh_ic = @(x) flory_ic(x, a, u0);
 fh_bc = @(xl, ul, xr, ur, t) flory_bc(xl, ul, xr, ur, t, u0);
-fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, a, b, c, u0);
+fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, a, b, e, c, u0);
 sol = pdepe(0, fh_pde, fh_ic, fh_bc, x, t);
 %% Plotting
 figure(1); hold on;
 for i = 1:length(t)
-    cla; xlim([49, 53]); ylim([0, 1.5]);
-    plot(x, phi_tot(x, a, b, u0)); plot(x, sol(i, :)); pause(0.03);
+%     i = 800;
+    cla; xlim([49, 53]); ylim([0, 0.7]); 
+    ax = gca;
+    ax.FontSize = 16;
+    xlabel('position'); ylabel('volume fraction');
+    plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 2, 'LineStyle', '--'); 
+    plot(x, sol(i, :), 'LineWidth', 2); pause(0.06);
+% %     print([num2str(i),'.png'],'-dpng')
 end
 
 %% Plot and check derivatives of pt
 figure; hold on;
-x = linspace(40, 60, 100);
-plot(x, phi_tot(x, -50, 0.25));
-plot(x, gradient_analytical(x, -50, 0.25));
-
+x = linspace(40, 60, 10000);
+plot(x, phi_tot(x, a, b, e, u0));
+plot(x, gradient_analytical(x, a, b, e));
+plot(x(1:end-1)+mean(diff(x))/2, ...
+     diff(phi_tot(x, a, b, e, u0)/mean(diff(x))));
+plot(x, gamma0(x, a, b, e));
+max(gamma0(x, a, b, e))/min(gamma0(x, a, b, e))
 %% Function definitions for pde solver
-function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, c_p, u0)  
+function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, e, c_p, u0)  
 % Solve with full ternary model. Analytical derivatives.
 % pt ... phi_tot
 % gra_a ... analytical gradient of phi_tot
 
-pt = phi_tot(x, a, b, u0);
-gra_a = gradient_analytical(x, a, b);
+pt = phi_tot(x, a, b, e, u0);
+gra_a = gradient_analytical(x, a, b, e);
+g0 = gamma0(x, a, b, e);
 c = c_p;
-f = ((u0+1.3)-pt)/pt*(pt*dudx-u*gra_a);
+f = g0*(1-pt)/pt*(pt*dudx-u*gra_a);
 s = 0;
 end
 
@@ -61,10 +72,14 @@ function [pl,ql,pr,qr] = flory_bc(xl, ul, xr, ur, t, u0)
     qr = 0;
 end
 
-function p = phi_tot(x, a, b, u0)
-    p = (tanh(-(x+a)/b)+1)/2+u0;
+function g0 = gamma0(x, a, b, e)
+    g0 = 10*e*(tanh((x+a)/b)+1)/2+0.001;
+end
+
+function p = phi_tot(x, a, b, e, u0)
+    p = e*(tanh(-(x+a)/b)+1)/2+u0;
 end
 
-function grad = gradient_analytical(x, a, b)
-    grad = -(1-tanh(-(x+a)/b).^2)*1/b*0.5;
+function grad = gradient_analytical(x, a, b, e)
+    grad = -e*(1-tanh(-(x+a)/b).^2)/b*0.5;
 end