Convergence of a Lagrangian scheme for a compressible Naviers–Stokes model defined on a domain depending on time

This paper deals with the numerical resolution of the Navier–Stokes equations defined on a time dependent domain. We give an existence result for a fluid-structure interaction problem in which the boundary is governed by a thin plate operator. We propose to solve the fluid equations with the characteristics method. We approach the total derivative with a “regularized” finite difference scheme and we study the convergence of the discrete problem towards the continuous one.