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Abstract <p>In modern computing and engineering practice, the problems of numerical solution of the radiation/neutron transport equation are relevant. To describe the complex geometry of installations, it is most convenient to use grids of tetrahedra. The projection-characteristic method developed in recent years for solving the transport equation on tetrahedral grids has a third order of accuracy on smooth solutions. The presence of contact discontinuities in the properties of matter and the complex spatial geometry of devices while solving real problems is often associated with an absence of smoothness of the exact solution. Therefore, there is interest in exploring the possibility of preserving the advantages of the proposed method in the case of a nonsmooth solution. The well-known Kobayashi benchmark is chosen for the study, with the exact value of the total flow found at 22 spatial points. This paper also explores the possibility of calculating with satisfactory accuracy on a not excessively detailed grid using high-order approximation schemes.</p>

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Investigation of the Projection–Characteristic Method for Solving the Transport Equation on the Kobayashi Benchmark

  • 期刊论文

  • 发表日期：

    2025年8月31日

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  • E. N. Aristova,
  • G. O. Astafurov

摘要

Abstract

In modern computing and engineering practice, the problems of numerical solution of the radiation/neutron transport equation are relevant. To describe the complex geometry of installations, it is most convenient to use grids of tetrahedra. The projection-characteristic method developed in recent years for solving the transport equation on tetrahedral grids has a third order of accuracy on smooth solutions. The presence of contact discontinuities in the properties of matter and the complex spatial geometry of devices while solving real problems is often associated with an absence of smoothness of the exact solution. Therefore, there is interest in exploring the possibility of preserving the advantages of the proposed method in the case of a nonsmooth solution. The well-known Kobayashi benchmark is chosen for the study, with the exact value of the total flow found at 22 spatial points. This paper also explores the possibility of calculating with satisfactory accuracy on a not excessively detailed grid using high-order approximation schemes.