On conditions for L2-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations
An explicit two-time-level and spatially symmetric finite-difference scheme approximating the 1D quasi-gasdynamic system of equations is studied. The scheme is linearized about a constant solution, and new necessary and sufficient conditions for the L2 -dissipativity of solutions of the Cauchy problem are derived, including, for the first time, the case of a nonzero background velocity depending on the Mach number. It is shown that the condition on the Courant number can be made independent of the Mach number. The results provide a substantial development of the well-known stability analysis of the linearized Lax–Wendroff scheme.