Monotonization of a highly accurate bicompact scheme for a stationary multidimensional transport equation

Abstract

A variant of a hybrid scheme for solving the nonhomogeneous stationary transport equation is constructed. A bicompact scheme of the fourth order approximation over all space variables and the first order approximation scheme from a set of short characteristic methods with interpolation over illuminated faces are chosen as a base. It is shown that the chosen first order approximation scheme is a scheme with minimal dissipation. A monotonic scheme is constructed by a continuous and homogeneous procedure in all the mesh cells by keeping the fourth approximation order in domains where the solution is smooth and maintaining a high level of accuracy in the domain of the discontinuity. The logical simplicity and homogeneity of the suggested algorithm make this method well fitted for supercomputer calculations.