Bicompact schemes for an inhomogeneous linear transport equation

Abstract

The bicompact finitedifference schemes co nstructed for a homogeneous linear transport equation for the case of the inhomogeneous transport equation are generalized. The equation describes the transport of particles or radiation in media. Using the method of lines, the bicompact scheme is constructed for the initial unknown function and the complementary unknown mesh func� tion defined as the integral average of the initial function with respect to space cells. The comparison of the calculation results of the proposed method and the conservativecharacteristic method is carried out. The latter can be assigned to the class of bicompact finitedifference schemes; however, this method is based on the idea of the redistribution of incoming fluxes from illuminated edges to unillu� minated edges.