Alternative to Unstructured Grids for Computing Gas Dynamic Flows AroundArbitrarily Complex Two-Dimensional Bodies

摘要

Within the shock-capturing community, the need to simulate flows aroundgeometrically complex bodies has resulted in an inexorable shift away from schemes which employ body-fitted grids to schemes which employ unstructured grids. Although unstructured grids are undeniably effective, in view of the increasing reliance placed on computational results, such a wholesale shift in mentality should give cause for concern. The concept of using several computer codes to cross check numerical results becomes ill-founded if all codes follow the same methodology. In this paper we describe an alternative approach for dealing with arbitrarily complex, two-dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.