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   Airfoil demo

/*    Copyright (c) 1995.  The Regents of the University of California.
                    All rights reserved.  */

func demo4 (mono=)
/* DOCUMENT demo4
         or demo4, mono=1
     solves for the flow past a 2D airfoil using Kutta-Jakowski theory.
     The colors represent static pressure (darker is lower pressure),
     red lines are streamlines.
     Solutions for various angles of attack are shown by animation.
     With the mono=1 keyword, only the streamlines are shown.  (On a
     monochrome terminal, the pressure makes the streamlines invisible.)
  require, "movie.i";
  local nx, ny;
  imax= 50;
  movie, display;
  display, imax;

func display(i)
  attack= 28.*double(imax-i)/(imax-1);
  solve, attack, 2.0, 0.2;
  if (i==1) {
    extern cn, cx;
    cn= 0.8*min(pressure);
    cx= max(pressure);
  limits, -2.8, 2.4, -2.4, 2.8;
  plmesh, z.im,z.re;
  if (!mono) plf, zncen(pressure), cmin=cn,cmax=cx;
  plc, potential.im, marks=0,color="red", levs=span(-2.5,3.5,33);
  plg,z.im(,1),z.re(,1), marks=0;
  return i<imax;

func solve (attack, chord, thick)
  extern w, z, potential, velocity, pressure; /* outputs */
  attack*= pi/180.;
  a= 0.5*chord;
  w= get_mesh(a, attack);
  /* the log(w) term adds just enough circulation to move the rear
     stagnation point to the trailing edge -- the Kutta condition */
  potential= jakowski(w, a) + 2i*a*sin(attack)*log(w);
  dpdw= 1.-(a/w)^2 + 2i*a*sin(attack)/w;
  emith= exp(-1i*attack);
  a= a*emith;
  b= thick*emith;  /* could add camber here too someday? */
  w-= b;
  a-= b;
  z= jakowski(w, a);
  dzdw= 1.-(a/w)^2;
  velocity= conj(dpdw/dzdw);
  pressure= 0.5*(1.0-abs(velocity)^2);

func get_mesh (a, attack)
  /* get a mesh in the w-plane
     -- the plane in which the airfoil is a circle
     the mesh splits at the point which will become the trailing edge */
  if (is_void(nx)) nx= 120;
  if (is_void(ny)) ny= 30;
  a= abs(a);
  theta= span(1.e-9, 2*pi-1.e-9, nx) - attack;
  r= a/span(1.0+1.e-9, 0.25, ny)(-,);
  return r*exp(1i*theta);

func jakowski (z, a)
  /* Jakowski transform - circle of radius a into slot of length 4a */
  return z + a*a/z;

func ijakowski (z, a)
  /* Inverse Jakowski - slot back into circle (unused here) */
  z*= 0.5;
  a= complex(a);
  sgn= sign((z*conj(a)).re);
  return z + sgn(z);