#! /usr/bin/env python
#
def uvp_spiral ( nu, rho, n, x, y, t ):

#*****************************************************************************80
#
## UVP_SPIRAL evaluates the Spiral Flow exact Navier Stokes solution.
#
#  Location:
#
#    http://people.sc.fsu.edu/~jburkardt/py_src/navier_stokes_2d_exact/uvp_spiral.py
#
#  Discussion:
#
#    This flow is known as a Spiral Flow solution.
#
#    The given velocity and pressure fields are exact solutions for the 2D 
#    incompressible time-dependent Navier Stokes equations over the unit square.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Maxim Olshanskii, Leo Rebholz,
#    Application of barycenter refined meshes in linear elasticity
#    and incompressible fluid dynamics,
#    ETNA: Electronic Transactions in Numerical Analysis, 
#    Volume 38, pages 258-274, 2011.
#
#  Parameters:
#
#    Input, real NU, the kinematic viscosity.
#
#    Input, real RHO, the density.
#
#    Input, integer N, the number of points at which the solution is to
#    be evaluated.
#
#    Input, real X(N), Y(N), the coordinates of the points.
#
#    Input, real T or T(N), the time coordinate or coordinates.
#
#    Output, real U(N), V(N), P(N), the velocity components and
#    pressure at each of the points.
#
  import numpy as np

  u = np.zeros ( n )
  v = np.zeros ( n )
  p = np.zeros ( n )

  u = ( 1.0 + nu * t ) * 2.0 \
    * x ** 2 * ( x - 1.0 ) ** 2 \
    * y * ( 2.0 * y - 1.0 ) * ( y - 1.0 )

  v = - ( 1.0 + nu * t ) * 2.0 \
    * x * ( 2.0 * x - 1.0 ) * ( x - 1.0 ) \
    * y ** 2 * ( y - 1.0 ) ** 2

  p = rho * y

  return u, v, p

def uvp_spiral_test ( ):

#*****************************************************************************80
#
## UVP_SPIRAL_TEST samples the Spiral Flow solution at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ( '' )
  print ( 'UVP_SPIRAL_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Spiral Flow:' )
  print ( '  Estimate the range of velocity and pressure' )
  print ( '  at the initial time T = 0, over the unit square.' )
  print ( '  Kinematic viscosity NU = %g' % ( nu ) )
  print ( '  Fluid density RHO = %g' % ( rho ) )

  n = 1000
  x_lo = 0.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  u, v, p = uvp_spiral ( nu, rho, n, x, y, t )

  print ( '' )
  print ( '           Minimum       Maximum' )
  print ( '' )
  print ( '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) ) )
  print ( '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) ) )
  print ( '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'UVP_SPIRAL_TEST:' )
  print ( '  Normal end of execution.' )
  return

def uvp_spiral_test2 ( ):

#*****************************************************************************80
#
## UVP_SPIRAL_TEST2 samples the Spiral Flow on the boundary at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 March 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  r8_lo = 0.0
  r8_hi = +1.0

  nu = 1.0
  rho = 1.0
  t = 0.0

  print ( '' )
  print ( 'UVP_SPIRAL_TEST2' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Spiral Flow:' )
  print ( '  Estimate the range of velocity and pressure' )
  print ( '  on the boundary' )
  print ( '  at the initial time T = 0, over the unit square.' )
  print ( '  Kinematic viscosity NU = %g' % ( nu ) )
  print ( '  Fluid density RHO = %g' % ( rho ) )

  n = 400

  x = np.zeros ( n )
  y = np.zeros ( n )

  x[0:100] = np.linspace ( r8_lo, r8_hi, 100 )
  y[0:100] = r8_lo

  x[100:200] = r8_hi
  y[100:200] = np.linspace ( r8_lo, r8_hi, 100 )

  x[200:300] = np.linspace ( r8_hi, r8_lo, 100 )
  y[200:300] = r8_hi

  x[300:400] = r8_lo
  y[300:400] = np.linspace ( r8_lo, r8_hi, 100 )

  u, v, p = uvp_spiral ( nu, rho, n, x, y, t )

  print ( '' )
  print ( '           Minimum       Maximum' )
  print ( '' )
  print ( '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) ) )
  print ( '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) ) )
  print ( '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'UVP_SPIRAL_TEST2:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  uvp_spiral_test ( )
  uvp_spiral_test2 ( )
  timestamp ( )