07-Jan-2022 16:42:31

burgers_steady_viscous_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test BURGERS_STEADY_VISCOUS.

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 = -8.25451e-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        0.193442
    32       0.0656687
    64     7.46236e-06
   128      -0.0858523
   256       0.0129652
   512      -0.0164546
  1024       0.0261832

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         0.35783
    32        0.360782
    64        0.341962
   128         0.35244
   256        0.332313
   512        0.344162
  1024        0.341841

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.
[Warning: Matrix is close to singular or badly scaled. Results may be
inaccurate. RCOND =  3.700743e-17.] 
[> In burgers_steady_viscous (line 103)
  In bsv_test08 (line 69)
  In burgers_steady_viscous_test (line 40)
  In run (line 91)
] 

  Saved plot to file "bsv_test08.png".

burgers_steady_viscous_test():
  Normal end of execution.

07-Jan-2022 16:43:22