Authors & Affiliations

Elshin A.V.
The Institute of Nuclear Power Engineering, “St. Petersburg Polytechnic University named after Peter the Great”, Sosnoby Bor, Russia


Currently there are quite a few methods for “straightforward” solution of neutron transport equation: the Monte Carlo method, discrete-ordinates method, the method of characteristics and others. The problem of the solution consists in the fact that for the real systems the dimension of the problem turns out to be tremendous, and the solution cannot be obtained promptly. The method of solution that is presently the most widely used is the homogenization method. This method reduces a high-dimension problem to a few problems of smaller dimensions. The neutron transport equation is solved only within the framework of a few (of different types) elementary cells of the reactor. These neutron distributions are used for the cell homogenization, i.e. a heterogeneous cell is replaced with abstract homogeneous medium “with the same multiplying and diffusion characteristics”, and the neutron distribution in the reactor on the whole is sought as the solution of a few-group diffusion equation in the system with piecewise-constant properties. The homogenization method is justified and specified by means of the surface harmonic method proposed in the last century, which in some way formalized the list of the required neutron distributions in elementary cells and the formulas to calculate coefficients of finite-difference few-group equations needed to calculate the reactor neutron distribution on the whole. This paper demonstrates that in the surface harmonic method the transfer to higher approximations (doing without diffusion approximation) is only carried out by increasing the dimension of equation matrices-coefficients (and thus, increasing the number of testing functions used to describe neutron distribution in elementary cells of the heterogeneous reactor).

Key words
Surface harmonic method, diffusion approximation, Monte Carlo method, neutron-transport equation, multigroup diffusion equations, heterogeneous reactor, homogenization method

Article Text (PDF, in Russian)


UDC 621.039.514

Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants", issue 4:12, 2014