We introduce a simple new Eulerian method for treatment of moving boundaries
in compressible fluid computations. Our approach is based on the extension
of the interface tracking method recently introduced in the context of
multifluids. The fluid domain is placed in a rectangular computational
domain of a fixed size, which is divided into Cartesian cells. At every
discrete time level, there are three types of cells: internal, boundary, and
external ones. The numerical solution is evolved in internal cells only. The
numerical fluxes at the cells near the boundary are computed using the
technique from [A. Chertock, S. Karni and A. Kurganov, M2AN Math. Model.
Numer. Anal., to appear] combined with a solid wall ghost-cell
extrapolation and an interpolation in the phase space. The proposed
computational framework is general and may be used in conjunction with one’s
favorite finite-volume method. The robustness of the new approach is
illustrated on a number of one- and two-dimensional numerical examples.