Bicompact schemes for an inhomogeneous linear transport equation
The bicompact finite-difference schemes constructed 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 function 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 conservative-characteristic method is carried out. The latter can be assigned to the class of bicompact finite-difference schemes; however, this method is based on the idea of the redistribution of incoming fluxes from illuminated edges to unilluminated edges.
Keywordstransport equation finite-difference schemes bicompact schemes conservative schemes Runge-Kutta methods redistribution of fluxes
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