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

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Oluwaseyi Aliu 2021-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/723748-colour-representation-of-three-matrices-entities-solid-rho1-and-rho2

回答： Anurag Ojha 2024-10-3

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

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Answer 1

Anurag Ojha 2024-10-3

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此回答的直接链接

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在 MATLAB Online 中打开

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');

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

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

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