### An Adaptive Cartesian Method for Computing the Three-Dimensional Unsteady Flow About Moving and Deforming Geometries

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Jason Hunt, University of Michigan
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An adaptive Cartesian method to solve inviscid-fluid interaction with moving and/or deforming geometries is presented. The class of flow problems in which bodies in the flow deform or move relative to each other remains a challenge for modern computational fluid dynamics (CFD) methods. Composite structured grids (the so-called Chimera technique) and fully unstructured grid techniques have had some successes computing flows about moving and deforming geometries, but problems arise when there is large relative motion between objects or if objects become close in proximity. The presented Cartesian approach, although limited to inviscid flow, can deal with the large relative motion problem without the grid shearing issues that arise on unstructured grids, and with the close proximity problem without the bookkeeping problems of the Chimera approach. This method appears promising for rapid-prototype inviscid-flow simulations.

The method consists of three main ingredients. First, the complex geometry is cut out from a Cartesian grid. Cells that intersect with the surface of the geometry are identified, subdivided to a prescribed limit, and then the intersected cells are "cut". Cells are cut by calculating the volume, centroid, and other geometric properties of the portion of the cell remaining in the flow domain. Second, the above process is performed on a block-of-cells basis instead of a cell-by-cell basis and is kept track of via an oct-tree data structure. This block adaptivity permits less frequent flow adaptation and is more amenable to parallelization. Finally, an inviscid finite-volume flow solver along with cell merging is used to perform time-accurate simulations with complex-geometry motion. Cell merging - combining several smaller cells into a single larger cell - is used to lessen time-step restrictions due to very tiny cut-cells and to enable the simulation of flow with body motion.

**Abstract Author(s): **Jason D. Hunt and Kenneth G. Powell