NONLOCAL STABILITY CONDITIONS OF THE "CREST" DIFFERENCE SCHEME FOR I-D GAS DYNAMICS WITH LAGRANDIAN VARIABLES

Yu. A. Bondarenko, V. V. Zmushko, А. M. Stenin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1984. Вып.3. С. 9-12.

      The linearized difference scheme, "Crest", is used to describe a method for obtaining nonlocal and asymptotically exact stability conditions (with a mesh point number tending to infinity) from initial data in the presence of local inhomogeneity in the scheme coefficients. A case of region-by-region computation and that of one small cell, compared to the rest, are considered. Smeared shock wave stability is examined for an artificial quadratic viscosity.

      The paper describes a linearly approximated estimation of the Crest-type difference scheme stability for solving 2-D gas dynamics equations with Lagrangian variables on arbitrary rectangular meshes in terms of artificial viscosity in the case where a pressure for the first boundary part and a normal velocity component for the second are given. For a time step, sufficient stability conditions close to exact ones are obtained in the form of inequalities to efficiently account the cell shapes, the grid nonuniformity, viscosity and sound speed variability along with boundary condition types. A weak instability is revealed which depends on the grid configuration near the boundary and a scheme modification is given with such instability removed.