Asymptotic expansion of a difference solution in the neighborhood of strong discontinuity

The method of construction an asymptotic expansion of a difference solution in the neighborhood of strong discontinuity is proposed. The method is based on the concept of the determining coefficient of an asymptotic expansion, which is used to construct a nonclassical differential approximations of difference scheme. The method is described by using general form of explicit two-level in time linear difference scheme approximating the linear transport equation. Asymptotic expansions of the difference solution are constructed for the scheme with the artificial viscosity for different values of viscosity coefficient. It is shown that the structure of the difference solution at the strong discontinuity is adequate accuracy described by the constructed expantions.