Verification method of Monte Carlo codes for transport processes with arbitrary accuracy.

Area of Science:

• Computational Physics
• Applied Mathematics
• Optical Science

Background:

• Monte Carlo methods are essential for simulating particle transport, including photon propagation in turbid media and neutron scattering.
• These methods are considered a gold standard for solving the radiative transport equation, particularly in complex geometries.
• Verification of these codes is critical for reliable scientific results, especially in fields like tissue optics.

Purpose of the Study:

• To present a robust method for verifying Monte Carlo codes used in simulating random walks in complex media.
• To demonstrate that this verification can be achieved with arbitrary accuracy.
• To provide a tool for assessing the accuracy of Monte Carlo simulations, particularly for boundary treatments.

Main Methods:

• The method leverages the law of average path length invariance for particles entering a medium with Lambertian distribution and no annihilation.
• Statistical tests are employed to assess the accuracy of the Monte Carlo code.
• The approach is general and applicable to various scattering and geometrical properties, including refractive index mismatches.

Main Results:

• The invariance of average path length provides a known expected value irrespective of medium complexity.
• The accuracy of Monte Carlo codes can be reliably assessed using simple statistical tests.
• Verification up to the sixth decimal digit was achieved for a tissue optics Monte Carlo code on a standard computer.

Conclusions:

• The presented method offers a powerful and accurate way to verify Monte Carlo codes for random walks.
• It serves as a fundamental tool for ensuring the reliability of simulations in complex geometries.
• The method allows for verification without needing to simplify geometries or scattering properties.