On enlarged sufficient conditions for L^2-dissipativity of linearized explicit schemes with regularization for 1D gas dynamics systems of equations

P. 53–67.

Zlotnik A.

We study an explicit two-level in time and three-point symmetric in space finite-difference scheme for 1D barotropic and full gas dynamics systems of equations. The scheme is a linearization at a constant background solution (with an arbitrary velocity) of finite-difference schemes with general viscous regularization. We enlarge recently proved sufficient conditions (on the Courant-like number) for $L^2$-dissipativity in the Cauchy problem for the schemes by deriving new bounds for the commutator of matrices of viscous and convective terms. We deal with the case of a kinetic regularization in more detail and specify sufficient conditions in this case where the mentioned matrices are closely connected. Importantly, these new sufficient conditions rapidly tend to the known necessary ones as the Mach number grows. Also several forms of setting a regularization parameter are considered.

Keywords: explicit finite-difference scheme, 1D gas dynamics equations, L^2-dissipativity, viscous regularization, commutator of matrices of viscous and convective terms, Mach number

In book

Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5

Vol. 333. , Springer, 2020.