Some Benchmark Results in Spherical Media Radiative Transfer Problems

The discrete eigenvalues for varying c and b 1 are given in Table S1. These eigenvalues are the numerical solutions of Eq. ( 5) in the main paper "Some numerical results of the albedo problem in spherical geometry with linearly anisotropic scattering". We use the FindRoot command, which runs with the Newton-Raphson method, to find these eigenvalues.In Figures 1-8 the albedo value is plotted against the scattering coefficient b 1 , in Figures 9 and 10 it is plotted against secondary neutron number c, in Figures 11-14 it is plotted against the radius of the solid homogeneous sphere R, and in Figures 15 and 16 it is plotted against N . In Figure 15, we calculate the albedo values from N = 0 to N = 8 for the H N method, while in Figure 16 we calculate the albedo values from N = 500 to N = 8000 for the SVD method.We see that the albedo values decrease along the scattering coefficient −0.3 ≤ b 1 ≤ 0.3 at all c and R values from c = 0.1 to c = 0.999 and R = 1 to R = 10. This decrease can be seen in Figures 1-8. However the albedo values increase along the number of secondary neutrons 0.1 ≤ c ≤ 0.999 at all b 1 and R values from b 1 = −0.3 to b 1 = 0.3 and R = 1 to R = 10. This increase can be seen in Figures 9 and 10. Moreover the albedo values decrease along the radius of the solid homogeneous sphere 1 ≤ R ≤ 10 at all c and b 1 values from c = 0.1 to c = 0.999 and b 1 = −0.3 to b 1 = 0.3. This decrease can be seen in Figures 11-14.

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Some Benchmark Results in Spherical Media Radiative Transfer Problems

Cited by 4 publications

References 31 publications

Integral Equations in the Kinetic Theory of Gases and Related Topics

Integral Equations in the Kinetic Theory of Gases and Related Topics

Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering

Some Numerical Results of the Albedo Problem in Spherical Geometry with Linearly Anisotropic Scattering

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