Communications in Mathematical Sciences
Volume 6 (2008)
A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries
Pages: 531 – 556
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.
Compressible Euler equations; ghost-cell extrapolation; moving boundaries; semi-discrete finite-volume schemes
2010 Mathematics Subject Classification
35L65, 65M99, 76N99