How can I change a variable and collect an vector of outputs?

Hello! I'm trying to figure out a way that I can vary V, and recieve an array of dc values that I can plot. Something about the nature of how dc is being obtained here is really throwing me off.

I've tried messing around with functions, whiles, and fors but I can't seem to make it work how I want it to. Any help is greatly appriciated!

Here's my code so far:

% process Parameters
V = 10 % S/L interface velocity in microns/sec

% 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

Answer 1

[Star Strider]

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

V = 10

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)

Result = 10x2 table
    Vv    dcv 
    __    ____

     2    0.52
     4    0.64
     6    0.69
     8    0.71
    10    0.73
    12    0.74
    14    0.75
    16    0.76
    18    0.76
    20    0.77

figure
plot(Vv, dcv)
grid
xlabel('V')
ylabel('dc')

.

[Charlie Rideout]

This makes a lot of sense! Yes absolutely, thank you! For some reason I was stuck on the idea of varying V as a variable... I need to get back into the habit of treating everything as a matrix or vector. Cheers!

[Star Strider]

As always, my pleasure!

Answer 2

[Torsten]

V_array = 0.5:0.1:20;
% 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
% Boundary Conditions
c_field(1) = c0 / k;
c_field(n) = c0;
c_field_update = c_field;
% Solver controls
tol = 1e-8; % Sets the tolerance for stopping the iteration
for j = 1:numel(V_array)
  V = V_array(j);
  F0 = 0.5*dx*D/V; % Finite Difference Coefficient
  err = 1; % sets starting value to check against tol
  % Solver
  while err > tol
    % 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(j) = idx*dx; % solute boundary layer thickness in microns
end
plot(V_array,dc)

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