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