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13-May-2025 11:25:28

burgers_steady_viscous_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  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
  Graphics saved as "bsv_test01.png".

  U(X0) = 0 estimated at X0 = -1.66533e-13

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
[Warning: Matrix is close to singular or badly scaled. Results may be
inaccurate. RCOND =  3.435153e-18.] 
[> In burgers_steady_viscous (line 103)
In bsv_test02 (line 43)
In burgers_steady_viscous_test (line 29)
In run (line 91)
] 

BURGERS_STEADY_VISCOUS - Warning!
  The Newton iteration did not converge.

  Graphics saved as "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

  Graphics saved as "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      -0.0370461
    32      0.00318899
    64      -0.0621577
   128       0.0352272
   256      0.00460491
   512        0.032562
  1024       0.0179594

bsv_test07():
  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        0.358343
    32        0.369498
    64        0.360916
   128        0.343474
   256        0.346907
   512        0.343817
  1024        0.344201

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".
  Graphics saved as "tanh_plot.png"

burgers_steady_viscous_test():
  Normal end of execution.

13-May-2025 11:26:20