计算流体力学原理规范化变量图。

% This program generates Fig. 4.9  in the book
% ......................Input.....................................

kappa = [-1  0  1/3  1/2  1  1/3];

% .....................End of input...............................
figure(1), clf

for j = 1:6    % Diagrams will be plotted for 6 schemes

x = 0.0:0.01:1.0;

y = (1 - kappa(j)/2)*x + (1+kappa(j))/4; % Characteristic of kappa-scheme

subplot(2,3,j), hold on

plot(x,y,'--'), axis([0.0  1.2  0.0 1.2])
xx = 0.0:0.01:0.5; y = 2*xx;       % Plot of dotted triangle

plot(xx,y,':'), plot(x,x,':')

xx = 0.5:0.01:1.0; y = ones(length(xx)); plot(xx,y,':'), plot(0.5,0.75,'o')

end
for j = 1:5  % Piecewise cubic-parabolic characteristic for general kappa scheme

subplot(2,3,j), hold on, title(['kappa = ',num2str(kappa(j))])

xx = 0.0:0.01:0.5; y = 2*xx +(kappa(j)-1)xx.^2 - 2kappa(j)xx.^3;

plot(xx,y)

xx = 0.5:0.01:1.0; z = xx - ones(1,length(xx));

if kappa(j) >= 0

y = ones(1,length(xx)) + 0.5kappa(j)*z + (kappa(j)-1)*z.^2;

else

y = ones(1,length(xx)) - (kappa(j)+1)z.^2 - 2kappa(j)*z.^3;

end

plot(xx,y)

end
subplot(2,3,6)    % Piecewise linear scheme

hold on, title(['PL'])

xx = 0.0:0.01:1.0; y=xx; kapfix = 1/3;

for j = 1:length(xx)

f1 = max(min(2xx(j),1),min(max(2xx(j),1),xx(j)));

f2 = (1-0.5*kapfix)xx(j) + 0.25(1+kapfix);

y(j) = max(min(f1,f2),min(max(f1,f2),xx(j)));

end

plot(xx,y)

% This program generates Fig. 4.9  in the book

% ......................Input.....................................

kappa = [-1  0  1/3  1/2  1  1/3];

% .....................End of input...............................
figure(1), clf

for j = 1:6    % Diagrams will be plotted for 6 schemes

x = 0.0:0.01:1.0;

y = (1 - kappa(j)/2)*x + (1+kappa(j))/4; % Characteristic of kappa-scheme

subplot(2,3,j), hold on

plot(x,y,'--'), axis([0.0  1.2  0.0 1.2])
xx = 0.0:0.01:0.5; y = 2*xx;       % Plot of dotted triangle

plot(xx,y,':'), plot(x,x,':')

xx = 0.5:0.01:1.0; y = ones(length(xx)); plot(xx,y,':'), plot(0.5,0.75,'o')

end
for j = 1:5  % Piecewise cubic-parabolic characteristic for general kappa scheme

subplot(2,3,j), hold on, title(['kappa = ',num2str(kappa(j))])

xx = 0.0:0.01:0.5; y = 2*xx +(kappa(j)-1)xx.^2 - 2kappa(j)xx.^3;

plot(xx,y)

xx = 0.5:0.01:1.0; z = xx - ones(1,length(xx));

if kappa(j) >= 0

y = ones(1,length(xx)) + 0.5kappa(j)*z + (kappa(j)-1)*z.^2;

else

y = ones(1,length(xx)) - (kappa(j)+1)z.^2 - 2kappa(j)*z.^3;

end

plot(xx,y)

end
subplot(2,3,6)    % Piecewise linear scheme

hold on, title(['PL'])

xx = 0.0:0.01:1.0; y=xx; kapfix = 1/3;

for j = 1:length(xx)

f1 = max(min(2xx(j),1),min(max(2xx(j),1),xx(j)));

f2 = (1-0.5*kapfix)xx(j) + 0.25(1+kapfix);

y(j) = max(min(f1,f2),min(max(f1,f2),xx(j)));

end

plot(xx,y)