Review of numerical computation of compressible flows with artificial interfaces

In Computational Fluid Dynamics, it is very often to use a composite grid for various purposes including easy meshing of a complex geometry, parallel computing, local mesh refinement, or treating different flows with different physical models, and using different numerical methods. All these methods have a common feature: they have internal artificial interfaces at which one needs to define interface conditions. In this paper, we first give a review on the current status of this subject with emphasis on compressible flows. Then two problems will be discussed in details. The first is for the overlapping grid approach due to its wide popularity for treating complex geometry and for parallel computing. The second is concerned with continuum/DSMC matching since this is a hot topic of current interest. A two dimensional computation is also performed to study the transmission of a shock wave across an overlapping grid interface.