chapter5_6.m

% LBM- 2-D2Q5a, diffusion equation, note that c2=1/3, w0=2/6, others 1/6
clear
m = 501; n = 501;
xl = 1.0; yl = 1.0;
dx = xl / (m - 1.0); dy = yl / (n - 1.0);
w0 = 2 ./ 6.;
w = 1 ./ 6.;
c2 = 1 ./ 3.;
dx = 1.0;
f0 = zeros(m, n); f1 = zeros(m, n); f2 = zeros(m, n); f3 = zeros(m, n); f4 = zeros(m, n);
rho = zeros(m, n); x = zeros(m); y = zeros(n); fluxq = zeros(m); flux = zeros(m);
Tm = zeros(m); Z = zeros(n, m);
x(1) = 0.0; y(1) = 0.0;

for i = 1:m - 1
    x(i + 1) = x(i) + dx;
end

for j = 1:n - 1
    y(j + 1) = y(j) + dy;
end

alpha = 0.25;
omega = 1 / (3 .* alpha + 0.5);
twall = 1.0;
nstep = 400;

for i = 1:m
    f0(i, j) = w0 * rho(i, j);
    f1(i, j) = w * rho(i, j);
    f2(i, j) = w * rho(i, j);
    f3(i, j) = w * rho(i, j);
    f4(i, j) = w * rho(i, j);
end

%Collision:
for k1 = 1:nstep

    for j = 1:n

        for i = 1:m
            feq0 = w0 * rho(i, j);
            feq = w * rho(i, j);
            f0(i, j) = (1 .- omega) * f0(i, j) + omega * feq0;
            f1(i, j) = (1 .- omega) * f1(i, j) + omega * feq;
            f2(i, j) = (1 .- omega) * f2(i, j) + omega * feq;
            f3(i, j) = (1 .- omega) * f3(i, j) + omega * feq;
            f4(i, j) = (1 .- omega) * f4(i, j) + omega * feq;
        end

    end

    % Streaming:
    for j = 1:n

        for i = 1:m - 1
            f1(m - i + 1, j) = f1(m - i, j);
            f2(i, j) = f2(i + 1, j);
        end

    end

    for i = 1:m

        for j = 1:n - 1
            f3(i, n - j + 1) = f3(i, n - j);
            f4(i, j) = f4(i, j + 1);
        end

    end

    %Boundary condition:
    for j = 1:n
        f1(1, j) = twall - f2(1, j) - f0(1, j) - f3(1, j) - f4(1, j);
        f3(m, j) = -f1(m, j) - f0(m, j) - f2(m, j) - f4(m, j);
    end

    for i = 1:m
        f3(i, 1) = f3(i, 2);
        f4(i, n) = -f0(i, n) - f3(i, n) - f2(i, n) - f1(i, n);
    end

    for j = 1:n

        for i = 1:m
            rho(i, j) = f1(i, j) + f2(i, j) + f0(i, j) + f3(i, j) + f4(i, j);
        end

    end

end

%rotating matrix for contour plotting
for j = 1:n

    for i = 1:m
        Z(j, i) = rho(i, j);
    end

end

for i = 1:n
    Tm(i) = rho(i, (n - 1) / 2);
end

figure(1)
plot(x, Tm)
xlabel("X")
ylabel("T")
figure(2)
contour(Z)
% title("Flux")
% xlabel("X")
% ylabel("Flux")