ON THE CONSTRUCTION OF A MONOTONE DIFFERENCE APPROXIMATION SCHEME FOR THE P_{1}EQUATION SYSTEM
A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2017. Вып.1. С. 3045.
In a nonstationary radiation transport problem, the P_{1}approximation leads to a hyperbolic system of equations and its solution causes significant difficulties of constructing a monotone difference scheme of the second approximation order. In a multidimensional case, one fails to construct a monotone scheme even of the first order of approximation for hyperbolic equation systems. The difficulties of constructing monotone schemes for the P_{1}approximation can be explained by the fact that the method of spherical harmonics has the wave effect and may give negative solutions in curved an multidimensional geometries for any P_{n}expansion. The second approximation order and an improved monotone behavior can be achieved by replacing the monotonicity preservation requirement by the requirement of a reduced full variation in nonlinear TVDschemes. The objective of work was to study possible variants of constructing monotone difference approximation schemes for the P_{1}equation system by the example of two schemes. Keywords: radiation transport, TVDreconstruction, P_{1}approximation.
