TFS METHOD. ITS TESTING ON STATIONARY 1D TRANSFER PROBLEMS
V. V. Evdokimov, I. A. Nizamova
VANT. Ser.: Mat. Mod. Fiz. Proc 2017. Вып.4. С. 32-47.
An approach to the scheme construction to solve the equation of transfer in kinetic approximation is offered. An approach to the scheme design to solve a transfer equation in kinetic approximation is described. An approximation scheme allowing explicitly express unknown values of the particles at the outlet from the cell is taken as the basic one. Then the cells are symbolically subdivided into sub-cells and the solution as a function of initial and boundary conditions is obtained for each sub-cell in series. The sum of all outgoing fluxes produces the expression for the flux at the output from the initial cell. The size of sub-cells is selected in such a way that the condition of positive approximation scheme is met. The number of sub-cells can strive to infinity; in this case we have a limit option of the scheme. The suggested approach to the scheme construction is called a TFS-method. Implementation of a TFS-method is considered for designing the scheme to solve the equation of neutron transfer in 1D stationary case. The computation results of two 1D stationary problems using a new scheme are given and they are compared with the results produced by known DD- and St-schemes. Keywords: TFS-method, transfer equation, difference schemes, testing, stationary transfer problems, DD-scheme, St-scheme, Reed test.
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