Linear quasi-monotonous and hybrid grid-characteristic schemes for the numerical solution of linear acoustic problems

The system of linear acoustic equations is hyperbolic. It describes the process of the acoustic wave propagation in deformable media. An important property of the schemes used for the numerical solution is their high approximation order. This property allows one to simulate the perturbation propagation process over sufficiently large distances. Another important property is monotonicity of the schemes used, which prevents the appearance of non-physical solution oscillations. In this paper, we present linear quasi-monotone and hybrid grid-characteristic schemes for a linear transport equation and a one-dimensional acoustic system. They are constructed by a method of analysis in the space of unknown coefficients proposed by A.S. Kholodov and a grid-characteristic monotonicity criterion. Wide spatial stencils with five to seven nodes of the computational grid are considered. Reflection of a longitudinal wave with a sharp front from the interface between media with different parameters is used to compare the numerical solutions.