A Two-Dimensional Conservation Laws Scheme for Compressible Flows with Moving Boundaries

✍ Scribed by J. Falcovitz; G. Alfandary; G. Hanoch

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 419 KB
• Volume: 138
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5808

✦ Synopsis

The generalized Riemann problem (GRP) scheme for the hydrodynamic conservation laws is extended to a two-dimensional moving boundary tracking (MBT) configuration, aimed at treating time-dependent compressible flows with moving (impermeable) boundary surfaces. A Strang-type operator splitting is employed for the integration of the conservation laws. The boundary motion is also split into Cartesian components that are taken with the respective operator-split integration phases. The conservation laws in boundary cells are integrated by a finite-volume scheme that accounts for changing mesh geometry (cell volume and side area through which mass, momentum, and energy fluxes are taken). The central feature of the scheme is the algorithms for evaluating the changing mesh geometry at boundary cells. These algorithms are based on a ''decomposition rule'' for evaluating polygon intersection area, which has been used extensively for rezoning in hydrocodes over the past decades. The decomposition rule is combined with the Cartesian splitting of the boundary motion, producing algorithms for the integration of conservation laws in boundary cells that are both consistent and simple. Consistency is taken to mean that the scheme produces an exact solution in the case of a uniform motion of the fluid and the boundary (common velocity). An illustrative example of shock lifting of a light-weight cylinder is presented.