A peer-reviewed journal published by K. N. Toosi University of Technology

Document Type : Research Article


Faculty of Engineering, Shahed University, P.O. Box 33191-18651, Tehran, Iran


The estimation of flux in radiation transport Monte Carlo problems needs to calculate the volumes and surface areas of the geometric regions. The particle flux is often estimated as the track length per unit volume or the number of particles crossing a surface per unit area in Monte Carlo transport problems. Various representations such as constructive solid geometry (CSG), boundary representation (B-Rep), and combinatorial geometry (CG) are proposed in the literature for geometry modeling and calculation of surface area and volume. MCNP series and OpenMC as Monte Carlo particle transport codes utilize CG modeling and are not able to calculate surface area as well as volume for non-rotationally symmetric or non-polyhedral cells. In this work, a comprehensive approach based on the Cauchy-Crofton formula using the Monte Carlo method has been implemented to the radiation transport codes as an extra module for computing surface area and volume of complex geometries. We used a random sampling procedure to create the required probe lines and points in the computational approach. The results show that this method can accurately compute surface areas and volumes of complex geometries with a relative error of less than 0.1% and a short computation time of a few seconds, which is not achievable with the cuurent MCNP and OpenMC modules.


  • The proposed method can compute all types of surface areas and volumes for complex geometries.
  • Reasonable accuracy and precision were obtained in a relatively short computational time.
  • The presented modules can be used effectively in any Monte Carlo-based code that employs CG geometry modelling.


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