One approach is to define a vector of ‘V’ values and then iterate.
Try something like this —
% process Parameters
V = 10 % S/L interface velocity in microns/sec
Vv = (2:2:20).';
for k1 = 1:numel(Vv)
V = Vv(k1);
% Material Parameters
c0 = 0.2; % Alloy composition
k = 0.28; % Partition Coefficient (conc solute in solid/ liquid)
D = 10; % Diffusivity in microns^2/sec
dc_tol = 1.01*c0; % Defines how close to c0 is acceptable
% Mesh Parameters
n = 500; % number of nodes
L = 5; % Length of nodes in microns
dx = L / n; % defining node spacing
x = linspace(0, L, n); % Mesh
% Initialise concentration field
c_field = ones(1, n)*c0; % Creates a field vector of intial concentrration
c_field_update = c_field;
% Initialise dc Field
dc_field = zeros(1, 100);
% Boundary Conditions
c_field(1) = c0 / k;
c_field(n) = c0;
% Solver controls
tol = 1e-3; % Sets the tolerance for stopping the iteration
err = 1; % sets starting value to check against tol
F0 = 0.5*dx*D/V; % Finite Difference Coefficient
% Solver
while err > tol
% Apply Boundary Conditions
c_field_update(1) = c_field(1);
c_field_update(n) = c_field(n);
% Finite Difference Scheme
for i = 2:(n-1)
c_field_update(i) = 0.5*(1+F0)*c_field(i+1)+0.5*(1-F0)*c_field(i-1);
end
% Compute Error
errVector = abs((c_field_update - c_field)./ c_field_update);
err = max(errVector);
% Update Concentration Field
c_field = c_field_update;
end
% Determine Solute Boundary Layer
% The ismembertol function gives number of nodes into the mesh for the first value that meets the dc_tol within a certain toleranmce, idx_tol)
idx_tol = 0.001*dc_tol;
[~, idx] = ismembertol(dc_tol, c_field, idx_tol);
dc = idx*dx; % solute boundary layer thickness in microns
dcv(k1,:) = dc;
end % ‘k’ Loop
Result = table(Vv,dcv)
figure
plot(Vv, dcv)
grid
xlabel('V')
ylabel('dc')
.
