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ON THE CONSTRUCTION OF A MONOTONE DIFFERENCE APPROXIMATION SCHEME FOR THE P1-EQUATION SYSTEM

A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2017. Вып.1. С. 30-45.

In a nonstationary radiation transport problem, the P1-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 P1-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 Pn-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 TVD-schemes. The objective of work was to study possible variants of constructing monotone difference approximation schemes for the P1-equation system by the example of two schemes.

Keywords: radiation transport, TVD-reconstruction, P1-approximation.








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