function [uv] = demo_ufunc(t,z,flo)
%DEMO_UFUNC  ODE file defining the velocities for demo1,demo2
%

% orig. by: cbm (24/01/2002)
% hacked on later by: djm, cbm
% current version: jrg, cbm (09/02/2002)
  
%  Scroll down to find out how to add your own problem...
  
global FLOW_TITLE DOMAIN;

switch flo
  case {1}
    % line vortex example, (Acheson, page12)
    k = 1;
    r2 = real(z).^2 + imag(z).^2;
  
    uv = (-k*imag(z)./r2) + i * (k*real(z)./r2);

    % global paramters for this problem:
    DOMAIN.left   = -1;  DOMAIN.right = 1; 
    DOMAIN.bottom = -1;  DOMAIN.top   = 1;
    FLOW_TITLE = ['\bf line vortex (irrotational)'];

  case {2}
    % solid body rotation (HW#1, Question 2, Acheson, page 24)
    GAMMA = 3;

    uv = -GAMMA*imag(z) + i * GAMMA*real(z);
    
    % global parameters for this problem:
    DOMAIN.left   = -1;  DOMAIN.right = 1; 
    DOMAIN.bottom = -1;  DOMAIN.top   = 1;
    FLOW_TITLE = ['\bf solid body rotation (rotational)'];

  case {3}
    % shear flow (Acheson, page12)
    BETA = 3;
  
    uv = BETA*imag(z);
    
    % global parameters for this problem
    DOMAIN.left   = -1;  DOMAIN.right = 1; 
    DOMAIN.bottom = -1;  DOMAIN.top   = 1;
    FLOW_TITLE = ['\bf parallel shear flow (rotational)'];

  case {4}
    % HW#0, problem 2 (flow around cylinder)
    B = 1;
    k = 2;

    x = real(z);
    y = imag(z);
    
    r2 = x.^2+y.^2;
    u = (r2 >= 1).*(  k*((1 - 1./r2) + (2*y.*y)./(r2.^2) + (B*y./r2))  );
    v = (r2 >= 1).*(  k*(-(2*x.*y)./(r2.^2) - (B*x)./r2)  );

    uv = u + i*v;
    
    % global parameters for this problem:
    DOMAIN.left   = -2;  DOMAIN.right = 2;
    DOMAIN.bottom = -2;  DOMAIN.top   = 2;
    FLOW_TITLE = ['\bf flow around a rotating cylinder (irrotational!)'];
    
  case {5}
    % add your own problem here...
    % see examples above

    error('you need to implement your own problem in demo_flow.m');
    
    % global parameters for this problem:
    DOMAIN.left   = -1;  DOMAIN.right = 1; 
    DOMAIN.bottom = -1;  DOMAIN.top   = 1;
    FLOW_TITLE = ['\bf my own problem'];
    
  otherwise
    error(['Flow case ' num2str(flo) ' not implemented']);
end