A method of computing complex two-dimensional gas-dynamic flows on variable-structure meshes is proposed. The medium is represented as a set of point particles and of domains surrounding the particles. These domains are so-called Dirichlet domains. Discretization of the equations is realized on a pattern formed from “Dirichlet neighbours”. To construct the difference scheme, the method of support operators is used; with this method, completely conservative schemes can be obtained. Results are given of two-dimensional computations on modelling a Rayleigh-Taylor instability in a closed rectangular vessel.