Conditions for $L^2$-dissipativity of linearized explicit difference schemes with regularization for $\mathrm{1D}$ barotropic gas dynamics equations

Explicit two-level in time and symmetric in space difference schemes constructed by approximating the 1D barotropic quasi-gas-/quasi-hydrodynamic systems of equations are studied. The schemes are linearized about a constant solution with a nonzero velocity, and, for them, necessary and sufficient conditions for the ${{L}^{2}}$ -dissipativity of solutions to the Cauchy problem are derived depending on the Mach number. These conditions differ from one another by at most twice. The results substantially develop the ones known for the linearized Lax–Wendroff scheme. Numerical experiments are performed to analyze the applicability of the found conditions in the nonlinear formulation to several schemes for different Mach numbers.