The convergence of a differential-difference scheme of gas dynamic equations in Lagrangian mass variables

Abstract

The convergence to a smooth solution of a completely conservative differential-difference scheme of gas dynamic equations in Lagrangian mass variables with sources (sinks) is investigated for the case of the ideal gas. It is proved that for the class of sufficiently smooth solutions of the differential problem the solution of the difference problem converges in the mesh norm L ₂ and that the rate of convergence is O(h ²).

Keywords:

• Lagrangian mass variables
• Difference schemes
• Partial differential equations