Colour representation of three matrices entities (SOLID, rho1 and rho2)

Dear friend,

Please I am solving a mixture of two fluids in a solid domain just as presented in the code below; I want a representation of the three parameters(SOLID,rho1 and rho2) with distinct colours in the same domain. Attached are two graphs (the one with two colours is the result I got, the result with three colours is what I want).

clear clc;close all;

% define numerical parameters

%new BounceBack<T,Descriptor>(0.5);

N=256;

nx=1*N; ny=N;

tau1=1; tau2=1; % relexation time

G=-1.5;

% define weight coefficient(D2Q9)

w0=4/9;

w1=1/9; w2=1/9; w3=1/9; w4=1/9;

w5=1/36; w6=1/36; w7=1/36; w8=1/36;

% initialize variable values in the field

c=1; %lattice speed

dt=1;% delta t

% solid capturing initialisation

SOLID=rand(nx+1,ny+1)>0.7;%extremely porous random domain

%SOLID = false( 1, nx, ny );

SOLID( 1, : ) = true;

SOLID( end, : ) = true;

SOLID( :, 1 ) = true;

SOLID( :, end ) = true;

%SOLID = find( SOLID );

% initialize distribution functions for two components

delta_rho=0.001*(1-2*rand(ny+1,nx+1));

rho1=1+delta_rho;

rho2=1-delta_rho;

% distribution function for component 1

f(:,:,1)=w1*rho1;

f(:,:,2)=w2*rho1;

f(:,:,3)=w3*rho1;

f(:,:,4)=w4*rho1;

f(:,:,5)=w5*rho1;

f(:,:,6)=w6*rho1;

f(:,:,7)=w7*rho1;

f(:,:,8)=w8*rho1;

f(:,:,9)=w0*rho1;

% distribution function for component 2

g(:,:,1)=w1*rho2;

g(:,:,2)=w2*rho2;

g(:,:,3)=w3*rho2;

g(:,:,4)=w4*rho2;

g(:,:,5)=w5*rho2;

g(:,:,6)=w6*rho2;

g(:,:,7)=w7*rho2;

g(:,:,8)=w8*rho2;

g(:,:,9)=w0*rho2;

for it=1:1000

% macropic properties

% calculate interaction body forces

rho1=sum(f,3); %density of fluid 1

rho2=sum(g,3); %density of fluid 2

rho_tot=rho1+rho2;% total local density

% body forces for conhension

F221_x=-rho1.*G.*(w1*circshift(rho2,[0,1])-w3*circshift(rho2,[0,-1])+w5*circshift(rho2,[-1,1])-w6*circshift(rho2,[-1,-1])...

-w7*circshift(rho2,[1,-1])+w8*circshift(rho2,[1,1]));

F221_y=-rho1.*G.*(w2*circshift(rho2,[-1 0])-w4*circshift(rho2,[1,0])+w5*circshift(rho2,[-1,1])+w6*circshift(rho2,[-1,-1])...

-w7*circshift(rho2,[1,-1])-w8*circshift(rho2,[1,1]));

F122_x=-rho2.*G.*(w1*circshift(rho1,[0,1])-w3*circshift(rho1,[0,-1])+w5*circshift(rho1,[-1,1])-w6*circshift(rho1,[-1,-1])...

-w7*circshift(rho1,[1,-1])+w8*circshift(rho1,[1,1]));

F122_y=-rho2.*G.*(w2*circshift(rho1,[-1 0])-w4*circshift(rho1,[1,0])+w5*circshift(rho1,[-1,1])+w6*circshift(rho1,[-1,-1])...

-w7*circshift(rho1,[1,-1])-w8*circshift(rho1,[1,1]));

% velocity field

u=(sum(f(:,:,[1 5 8]),3)-sum(f(:,:,[3 6 7]),3)+sum(g(:,:,[1 5 8]),3)-sum(g(:,:,[3 6 7]),3))./rho_tot+(F221_x+F122_x)./rho_tot./2;

v=(sum(f(:,:,[2 5 6]),3)-sum(f(:,:,[4 7 8]),3)+sum(g(:,:,[2 5 6]),3)-sum(g(:,:,[4 7 8]),3))./rho_tot+(F221_y+F122_y)./rho_tot./2;

% collision step

% calculate equilibrium distribution for fluid 1

feq(:,:,1)=w1*rho1.*(1+3*u/c+9/2*u.^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,2)=w2*rho1.*(1+3*v/c+9/2*v.^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,3)=w3*rho1.*(1+3*-u/c+9/2*u.^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,4)=w4*rho1.*(1+3*-v/c+9/2*v.^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,5)=w5*rho1.*(1+3*(u+v)/c+9/2*(u+v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,6)=w6*rho1.*(1+3*(-u+v)/c+9/2*(-u+v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,7)=w7*rho1.*(1+3*(-u-v)/c+9/2*(-u-v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,8)=w8*rho1.*(1+3*(u-v)/c+9/2*(u-v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

feq(:,:,9)=w0*rho1.*(1-3/2*(u.^2+v.^2)/c^2);

% for fluid 2

geq(:,:,1)=w1*rho2.*(1+3*u/c+9/2*u.^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,2)=w2*rho2.*(1+3*v/c+9/2*v.^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,3)=w3*rho2.*(1+3*-u/c+9/2*u.^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,4)=w4*rho2.*(1+3*-v/c+9/2*v.^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,5)=w5*rho2.*(1+3*(u+v)/c+9/2*(u+v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,6)=w6*rho2.*(1+3*(-u+v)/c+9/2*(-u+v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,7)=w7*rho2.*(1+3*(-u-v)/c+9/2*(-u-v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,8)=w8*rho2.*(1+3*(u-v)/c+9/2*(u-v).^2/c^2-3/2*(u.^2+v.^2)/c^2);

geq(:,:,9)=w0*rho2.*(1-3/2*(u.^2+v.^2)/c^2);

%calculate body force terms in collision step

% for fluid 1

F1(:,:,1)=w1*(1-1/2/tau1)*((6*u+3).*(F221_x)+-3*v.*(F221_y));

F1(:,:,2)=w2*(1-1/2/tau1)*(-3*u.*(F221_x)+(3+6*v).*(F221_y));

F1(:,:,3)=w3*(1-1/2/tau1)*((6*u-3).*(F221_x)+-3*v.*(F221_y));

F1(:,:,4)=w4*(1-1/2/tau1)*(-3*u.*(F221_x)+(-3+6*v).*(F221_y));

F1(:,:,5)=w5*(1-1/2/tau1)*((3+6*u+9*v).*(F221_x)+(3+9*u+6*v).*(F221_y));

F1(:,:,6)=w6*(1-1/2/tau1)*((-3+6*u-9*v).*(F221_x)+(3-9*u+6*v).*(F221_y));

F1(:,:,7)=w7*(1-1/2/tau1)*((-3+6*u+9*v).*(F221_x)+(-3+9*u+6*v).*(F221_y));

F1(:,:,8)=w8*(1-1/2/tau1)*((3+6*u-9*v).*(F221_x)+(-3-9*u+6*v).*(F221_y));

F1(:,:,9)=w0*(1-1/2/tau1)*(-3*u.*(F221_x)+-3*v.*(F221_y));

% for fluid 2

F2(:,:,1)=w1*(1-1/2/tau2)*((6*u+3).*(F122_x)+-3*v.*(F122_y));

F2(:,:,2)=w2*(1-1/2/tau2)*(-3*u.*(F122_x)+(3+6*v).*(F122_y));

F2(:,:,3)=w3*(1-1/2/tau2)*((6*u-3).*(F122_x)+-3*v.*(F122_y));

F2(:,:,4)=w4*(1-1/2/tau2)*(-3*u.*(F122_x)+(-3+6*v).*(F122_y));

F2(:,:,5)=w5*(1-1/2/tau2)*((3+6*u+9*v).*(F122_x)+(3+9*u+6*v).*(F122_y));

F2(:,:,6)=w6*(1-1/2/tau2)*((-3+6*u-9*v).*(F122_x)+(3-9*u+6*v).*(F122_y));

F2(:,:,7)=w7*(1-1/2/tau2)*((-3+6*u+9*v).*(F122_x)+(-3+9*u+6*v).*(F122_y));

F2(:,:,8)=w8*(1-1/2/tau2)*((3+6*u-9*v).*(F122_x)+(-3-9*u+6*v).*(F122_y));

F2(:,:,9)=w0*(1-1/2/tau2)*(-3*u.*(F122_x)+-3*v.*(F122_y));

% collision

f=f-1/tau1.*(f-feq)+F1;

g=g-1/tau2.*(g-geq)+F2;

%streaming

f(:,:,1)=circshift(f(:,:,1),[0,1]);

f(:,:,2)=circshift(f(:,:,2),[-1,0]);

f(:,:,3)=circshift(f(:,:,3),[0,-1]);

f(:,:,4)=circshift(f(:,:,4),[1,0]);

f(:,:,5)=circshift(f(:,:,5),[-1,1]);

f(:,:,6)=circshift(f(:,:,6),[-1,-1]);

f(:,:,7)=circshift(f(:,:,7),[1,-1]);

f(:,:,8)=circshift(f(:,:,8),[1,1]);

g(:,:,1)=circshift(g(:,:,1),[0,1]);

g(:,:,2)=circshift(g(:,:,2),[-1,0]);

g(:,:,3)=circshift(g(:,:,3),[0,-1]);

g(:,:,4)=circshift(g(:,:,4),[1,0]);

g(:,:,5)=circshift(g(:,:,5),[-1,1]);

g(:,:,6)=circshift(g(:,:,6),[-1,-1]);

g(:,:,7)=circshift(g(:,:,7),[1,-1]);

g(:,:,8)=circshift(g(:,:,8),[1,1]);

% add BC

%L

f(:,1,1)=f(:,nx+1,1);

f(:,1,5)=f(:,nx+1,5);

f(:,1,8)=f(:,nx+1,8);

g(:,1,1)=g(:,nx+1,1);

g(:,1,5)=g(:,nx+1,5);

g(:,1,8)=g(:,nx+1,8);

%R

f(:,nx+1,3)=f(:,1,3);

f(:,nx+1,6)=f(:,1,6);

f(:,nx+1,7)=f(:,1,7);

g(:,nx+1,3)=g(:,1,3);

g(:,nx+1,6)=g(:,1,6);

g(:,nx+1,7)=g(:,1,7);

%T

f(1,:,4)=f(ny+1,:,4);

f(1,:,7)=f(ny+1,:,7);

f(1,:,8)=f(ny+1,:,8);

g(1,:,4)=g(ny+1,:,4);

g(1,:,7)=g(ny+1,:,7);

g(1,:,8)=g(ny+1,:,8);

%B

f(ny+1,:,2)=f(1,:,2);

f(ny+1,:,5)=f(1,:,5);

f(ny+1,:,6)=f(1,:,6);

g(ny+1,:,2)=g(1,:,2);

g(ny+1,:,5)=g(1,:,5);

g(ny+1,:,6)=g(1,:,6);

if rem(it,5)==0

imagesc(rho1);

%imagesc(rho2);

%imagesc(solid);

fff=getframe;

axis equal off;

end

end

Answer 1

[Anurag Ojha]

Hey

To represent the three parameters (SOLID, rho1, and rho2) with distinct colors in the same domain, you can combine them into a single array where each parameter corresponds to a different channel in the RGB color model. For instance:

• Use SOLID as the red channel.
• Use rho1 as the green channel.
• Use rho2 as the blue channel.

This way, areas of the plot where all three variables are significant will appear as a combination of their respective colors. Below is a simplified code which I have written taking certain assumption. Kindly modify it as per your use case:

% Clear workspace and close all figures
clear;
clc;
close all;

% Define numerical parameters
N = 100;  % Grid size
nx = N;
ny = N;

% Initialize solid capturing: Randomly assign solid areas
SOLID = rand(nx, ny) > 0.7;  % Extremely porous random domain
% Add boundaries as solid
SOLID(1, :) = true;
SOLID(end, :) = true;
SOLID(:, 1) = true;
SOLID(:, end) = true;

% Initialize densities for fluid 1 (rho1) and fluid 2 (rho2)
delta_rho = 0.01 * (1 - 2 * rand(ny, nx));  % Small random perturbations
rho1 = 1 + delta_rho;  % Fluid 1 density
rho2 = 1 - delta_rho;  % Fluid 2 density

% Normalize the values for visualization
rho1_norm = (rho1 - min(rho1(:))) / (max(rho1(:)) - min(rho1(:)));
rho2_norm = (rho2 - min(rho2(:))) / (max(rho2(:)) - min(rho2(:)));
SOLID_norm = double(SOLID);  % Ensure SOLID is numeric

% Combine the parameters into an RGB image
% Red for SOLID, Green for rho1, Blue for rho2
RGB_image = cat(3, SOLID_norm, rho1_norm, rho2_norm);

% Display the RGB image
figure;
imagesc(RGB_image);
axis equal off;
title('Representation of SOLID, rho1, and rho2 in RGB');