04-Dec-2018 15:56:37

BURGERS_STEADY_VISCOUS_TEST
  MATLAB version.
  Test the BURGERS_STEADY_VISCOUS (BSV) library.

BSV_TEST01:
  Solution of steady viscous Burgers equation.

  Step  ||F(U)||

     0  0.9
     1  1.3177
     2  0.140345
     3  0.00158582
     4  1.58645e-07

  Saved plot to file "bsv_test01.png".

  U(X0) = 0 estimated at X0 = 2.13852e-14

BSV_TEST02:
  Solution of steady viscous Burgers equation.
  Consider a variety of values of viscosity nu.

  Using NU = 0.8
  Using NU = 0.4
  Using NU = 0.2
  Using NU = 0.1
  Using NU = 0.05
  Using NU = 0.025

BURGERS_STEADY_VISCOUS - Warning!
  The Newton iteration did not converge.

  Saved plot to file "bsv_test02.png".

BSV_TEST03:
  Solution of steady viscous Burgers equation.
  Vary the left boundary condition ALPHA around the value +1.

  Using ALPHA = 0.96
  Using ALPHA = 0.98
  Using ALPHA = 0.99
  Using ALPHA = 0.995
  Using ALPHA = 1
  Using ALPHA = 1.005
  Using ALPHA = 1.01
  Using ALPHA = 1.02
  Using ALPHA = 1.04

  Saved plot to file "bsv_test03.png".

BSV_TEST04:
  Solution of steady viscous Burgers equation.
  Vary the left boundary location A around the value -1.

  Using A = -1.04
  Using A = -1.02
  Using A = -1.01
  Using A = -1.005
  Using A = -1
  Using A = -0.995
  Using A = -0.99
  Using A = -0.98
  Using A = -0.96

  Saved plot to file "bsv_test04.png".

BSV_TEST05:
  For the Burgers equation on [A,B] with viscosity NU and 
  boundary conditions U(A)=ALPHA, U(B) = BETA,
  with ALPHA and BETA of opposite sign,
  let X0 be the point where the solution U changes sign.
  Sample and plot the functional relationship X0(ALPHA).

  Saved plot to file "bsv_test05.png".

BSV_TEST06:
  For the Burgers equation on [A,B] with viscosity NU and 
  boundary conditions U(A)=ALPHA, U(B) = BETA,
  with ALPHA and BETA of opposite sign,
  let X0 be the point where the solution U changes sign.
  Assume ALPHA is Gaussian with mean 0 and standard deviation 0.05.
  Estimate E(X0(ALPHA)) using M Gaussian samples.

     M    E(X0(ALPHA)) estimate

    16       0.0077358
    32        0.139994
    64       0.0734689
   128        0.036592
   256      -0.0103225
   512       0.0105753
  1024       0.0409696

BSV_TEST06:
  For the Burgers equation on [A,B] with viscosity NU and 
  boundary conditions U(A)=ALPHA, U(B) = BETA,
  with ALPHA and BETA of opposite sign,
  let X0 be the point where the solution U changes sign.
  Assume ALPHA is Gaussian with mean 0 and standard deviation 0.05.
  Estimate Var(X0(ALPHA)) using M Gaussian samples.

     M    Var(X0(ALPHA)) estimate

    16        0.321515
    32        0.340195
    64        0.358292
   128        0.331607
   256        0.354972
   512        0.355249
  1024        0.342429

BSV_TEST08:
  Compare BSV and BSV_UPWIND.
  Upwinding is a scheme which reduces the numerical oscillations
  that can occur as the viscosity in the Burgers equation is decreased.

  The distortion caused by upwinding is visible for N = 21, NU = 0.1.
  The oscillations caused by NOT upwinding are visible for N = 21, NU = 0.01.

  Saved plot to file "bsv_test08.png".

BURGERS_STEADY_VISCOUS_TEST
  Normal end of execution.

04-Dec-2018 15:58:53