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a guest Apr 23rd, 2019 61 Never
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  1. clearvars
  2. close all
  3.  
  4. OP = [.25 .25 7 7,];
  5.  
  6. xmin = -5;
  7. xmax = 5;
  8. ymin = -5;
  9. ymax = 5;
  10. spacing = 0.01;
  11.  
  12. %Define value for vortices and cross flow
  13. Gamma1 = -20;
  14. Gamma2 = 8;
  15.  
  16. U = 5;
  17. a = 0;
  18.  
  19. x = (xmin:spacing:xmax);
  20. y = (ymin:spacing:ymax);
  21.  
  22. xsize = numel(x);
  23. ysize = numel(y);
  24.  
  25. [x,y] = meshgrid(x,y);
  26.  
  27. %time step
  28. ts = 0.00001;
  29. dur = 0;
  30.  
  31. %Vortex center location
  32. yc1 = -1;
  33. xc1= -1;
  34. yc2 = 1;
  35. xc2 = 1;
  36.  
  37.  
  38. r1 = sqrt(((x-xc1).^2)+((y-yc1).^2));
  39. r2 = sqrt(((x-xc2).^2)+((y-yc2).^2));
  40.  
  41. %Psi defined for vortices and cross flow
  42. Psi1= (Gamma1*log(r1)./(2*pi));
  43.  
  44. Psi2 = Gamma2*log(r2)./(2*pi);
  45.  
  46. Psi3 = U*((-sind(a).*x) + (cosd(a).*y));
  47.  
  48. xloc1 = zeros(1,xsize); %x location of vortex 1
  49. yloc1 = zeros(1,ysize); %y location of vortex 1
  50.  
  51. xloc2 = zeros(1,xsize); %x location of vortex 2
  52. yloc2 = zeros(1,ysize); %y location of vortex 2
  53.  
  54.  
  55.  
  56. u1 = zeros(ysize,xsize);
  57. v1 = zeros(ysize,xsize);
  58.  
  59. dPsidy1 = zeros(ysize,xsize);
  60. dPsidx1 = zeros(ysize,xsize);
  61.  
  62. for i = 2:(ysize-1)
  63.     for j = 2:xsize-1
  64.         %The y value changes as you increase the row (so i)
  65.         %Essentially this is delta y over delta x
  66.         dPsidy1(i,j) = (Psi1(i+1,j) - Psi1(i-1,j) )/ (2*spacing);
  67.         dPsidx1(i,j) = (Psi1(i,j+1) - Psi1(i,j-1)) / (2*spacing);
  68.     end
  69. end
  70.  
  71. dPsidy2 = zeros(ysize,xsize);
  72. dPsidx2 = zeros(ysize,xsize);
  73.  
  74. for i = 2:(ysize-1)
  75.     for j = 2:xsize-1
  76.         %The y value changes as you increase the row (so i)
  77.         %Essentially this is delta y over delta x
  78.         dPsidy2(i,j) = (Psi2(i+1,j) - Psi2(i-1,j) )/ (2*spacing);
  79.         dPsidx2(i,j) = (Psi2(i,j+1) - Psi2(i,j-1)) / (2*spacing);
  80.     end
  81. end
  82.  
  83. u1 = dPsidy1;   %matrix of x velocity
  84. v1 = -1* dPsidx1; %matrix of y velocity
  85.  
  86. u1(u1>1000000) = 0;
  87. u1(u1<-1000000) = 0;
  88. v1(v1>1000000) = 0;
  89. v1(v1<-1000000) = 0;
  90.  
  91. for n1 = 1:(ysize)
  92.     for m1 = 1:(xsize)
  93.         xc2 = xc2 + (u1(n1, m1).*ts);
  94.         yc2 = yc2 + (v1(n1, m1).*ts);
  95.     end
  96. end    
  97. %totalv = (u.^2 + v.^2).^.5;
  98.        
  99. %hold on
  100. %contourf(x,y,Psi, 1000, 'LineStyle', 'none');
  101. %colormap
  102. %colorbar
  103. %h = colorbar;
  104. %title(h, '\psi')
  105. %hold on;
  106.  
  107.  
  108. %ph = streamslice(x,y,u1,v1);
  109.  
  110. %set(ph,'color','k');
  111.  
  112. %axis([xmin xmax ymin ymax]);
  113. %set(gcf,'Units','inches','OuterPosition',OP);
  114.  
  115. %title('Streamlines for vortices');
  116. %xlabel('x location');
  117. %ylabel('y location');
  118. %hold off
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