Comparison of the Efficiency of the Transport Equation Calculation Methods in Characteristics Variables

Abstract

Two efficient methods for numerical solving of 2D steady transport equation on the basis of transition to the characteristics variables in r-z-geometry have been suggested. These variables had been introduced by V.S.Vladimirov (1958, 1998) for neutron calculations in Soviet atomic project. The spatial and angular meshes are rigidly connected in classical differential variant of Vladimirov's method of long characteristics that is not convenient in many practical cases. The equation-solving algorithm is suggested with independent construction of these meshes. It allows us to resolve explicitly the structure of all logarithmical discontinuities of solution, which is immanent for heterogeneous problems with spherical and cylindrical geometry. Two variants of the method of characteristics have been suggested: method of short characteristics and its conservative modification. Their comparison has been carried out. It has been shown for test problems that possess exact solution that for rough meshes the conservative variant of the method allows the constructed solution to be of high accuracy, especially for quasi-diffusion tensor.

Keywords:

• Transport equation
• Quasi diffusion method
• Method of characteristics
• Logarithmical discontinuities

This work was accomplished with the financial support from Russian Foundation for Basic Research (grant No. 06-01-00549a).