L^2-диссипативность разностных схем для регуляризованных 1D баротропных уравнений движения газа при малых числах Маха

Математическое моделирование. 2021. Т. 33. № 5. С. 16–34.

Zlotnik A., Lomonosov T.

We study explicit two-level finite-difference schemes on staggered meshes for two known regularizations of 1D barotropic gas dynamics equations including schemes with discretizations in x that possess the dissipativity property with respect to the total energy. We derive criterions of L^2-dissipativity in the Cauchy problem for their linearizations at a constant solution with zero background velocity. We compare the criterions for schemes on non-staggered and staggered meshes. Also we consider the case of 1D Navier-Stokes equations without artificial viscosity coefficient. To analyze the case of the 1D Navier-Stokes-Cahn-Hilliard equations, we derive and verify the criterions for L^2-dissipativity and stability for an explicit finite-difference scheme approximating a non-stationary 4th-order in x equation that includes a 2nd-order term in x. The obtained criteria may be useful to compute flows at small Mach numbers.

Key words: -dissipativity, explicit finite-difference schemes, staggered meshes, gas dynamics equations, Navier-Stokes-Cahn-Hilliard equations.

Keywords: уравнения газовой динамики, regularized Navier-Stokes-Cahn-Hilliard equations, регуляризованные уравнения Навье-Стокса-Кана-Хилларда, явные разностные схемы, L^2-dissipativity, explicit finite-difference schemes, barotropic gas dynamics equations, staggered meshes, L^2-диссипативность, разнесённые сетки