add exerices sheets, worked example matlab scripts

uni/mmme/3086_computer_modelling_techniques/worked_example_matlab_scripts/l1_wx1.m

@@ -0,0 +1,65 @@
+% author: Akbar Alvi Rahman
+% Lecture 1 Worked Example 1 (Section 10.1)
+
+clear all; close all; clc
+
+% define physical constants
+L = 1;
+S = 0;
+conductivity = 400;
+Ta = 300;
+Tb = 320;
+
+% define numerical parameters
+n = 21;
+
+% grid generation
+x0 = linspace(0, L, 21);
+dx = L/(n-1);
+Dx = dx;
+DxB = Dx/2;
+
+% create matrix
+A = zeros(n, n);
+B = zeros(n, 1);
+
+A(1, 1) = 1; % Dirichlet boundary
+B(1) = Ta;
+
+A(n, n) = 1; % Dirichlet boundary
+B(n) = Tb;
+
+for i=2:n-1
+    A(i, i-1) = -conductivity/dx;
+    A(i, i) = 2*conductivity/dx;
+    A(i, i+1) = -conductivity/dx;
+
+    B(i) = 0;
+end
+
+T = A\B; % matrix backslash
+
+figure('color', 'w'); 
+plot(x0, T, 'rs');
+grid on;
+xlabel('x [m]'); ylabel('T [K]');
+hold on;
+
+% comparison with theoretical solution
+Tteo = Ta + (Tb-Ta)*x0/L;
+plot(x0, Tteo, 'k-');
+legend('backslash', 'Exact');
+error = mean(abs(T-Tteo')) % Tteo transposed by ' operator
+
+% check of residuals
+residual = sum(abs(B-A*T))/sum(abs(diag(A).*T)) % defined as |B-A*T|/|diag(A).T|
+
+% check of energy balance
+num=0; den = 0;
+
+for i=2:n-1
+    num = num+abs(-conductivity*(T(i)-T(i-1))/dx+conductivity*(T(i+1)-T(i))/dx); % sum(|q_w-q_e|)
+    den = den+abs(conductivity*(T(i)-T(i-1))/dx); % sum(|q_w|)
+end
+
+unbalance = num/den*100

uni/mmme/3086_computer_modelling_techniques/worked_example_matlab_scripts/l2_wx2.m

@@ -0,0 +1,68 @@
+% author: Akbar Alvi Rahman
+% Lecture 1 Worked Example 1 (Section 10.1)
+
+clear all; close all; clc
+
+% define physical constants
+L = 1;
+S = 0;
+conductivity = 400;
+Ta = 300;
+Tb = 320;
+
+Sp = -100;
+Sc = 5000;
+
+% define numerical parameters
+n = 21;
+
+% grid generation
+x0 = linspace(0, L, 21);
+dx = L/(n-1);
+Dx = dx;
+DxB = Dx/2;
+
+% create matrix
+A = zeros(n, n);
+B = zeros(n, 1);
+
+A(1, 1) = 1; % Dirichlet boundary
+B(1) = Ta;
+
+A(n, n) = 1; % Dirichlet boundary
+B(n) = Tb;
+
+for i=2:n-1
+    A(i, i-1) = -conductivity/dx;
+    A(i, i) = 2*conductivity/dx-Sp*Dx;
+    A(i, i+1) = -conductivity/dx;
+
+    B(i) = Sc*Dx;
+end
+
+T = A\B; % matrix backslash
+
+figure('color', 'w'); 
+plot(x0, T, 'rs');
+grid on;
+xlabel('x [m]'); ylabel('T [K]');
+hold on;
+
+% comparison with theoretical solution
+Tteo = Ta + (Tb-Ta)*x0/L;
+plot(x0, Tteo, 'k-');
+legend('backslash', 'Exact');
+error = mean(abs(T-Tteo')) % Tteo transposed by ' operator
+
+% check of residuals
+residual = sum(abs(B-A*T))/sum(abs(diag(A).*T)) % defined as |B-A*T|/|diag(A).T|
+
+% check of energy balance
+num=0; den = 0;
+
+for i=2:n-1
+    num = num+abs(-conductivity*(T(i)-T(i-1))/dx+conductivity*(T(i+1)-T(i))/dx); % sum(|q_w-q_e|)
+    den = den+abs(conductivity*(T(i)-T(i-1))/dx); % sum(|q_w|)
+end
+
+unbalance = num/den*100