Computation of Inviscid Compressible Flows About Arbitrary Geometries and Moving Boundaries.

The computational simulation of aerodynamic flows with moving boundaries has numerous scientific and practical motivations. In this work, a new technique for computation of inviscid, compressible flows about two-dimensional, arbitrarily-complex geometries that are allowed to undergo arbitrarily-complex motions or deformations is developed and studied. The computational technique is constructed from five main components: (i) an adaptive, Quadtree-based, Cartesian-Grid generation algorithm that divides the computational region into stationary square cells, with local refinement and coarsening to resolve the geometry of all internal boundaries, even as such boundaries move. The algorithm automatically clips cells that straddle boundaries to form arbitrary polygonal cells; (ii) a representation of internal boundaries as exact, infinitesimally-thin discontinuities separating two arbitrarily-different states. The exactness of this representation, and its preclusion of diffusive or dispersive effects while boundaries travel across the grid combines the advantages of Eulerian and Lagrangian methods and is the main distinguishing characteristic of the technique; (iii) a second-order-accurate Finite-Volume, Arbitrary Lagrangian-Eulerian, characteristic-based flow-solver. The discretization of the boundaries and their motion is matched with the discretization of the flux quadratures to ensure that the overall second-order-accurate discretization also satisfies The Geometric Conservation Laws; (iv) an algorithm for dynamic merging of the cells in the vicinity of internal boundaries to form composite cells that retain the same topologic configuration during individual boundary motion steps and can therefore be treated as deforming cells, eliminating the need to treat crossing of grid lines by moving boundaries. Cell merging is also used to circumvent the ``small-cell problem'' of non-boundary-conformal Cartesian Grids; and (v) a solution-adaptation algorithm for resolving flow features with large gradients or different length-scales, and for automatically tracking these features as they move. The components of the technique are described in detail, with emphasis on the treatment of moving boundaries. Computations are presented for verification, validation, and demonstration problems covering internal and external flows, and ranging from steady-state flows with stationary boundaries to unsteady flows with multiple length scales, moving boundaries, fluid-structure interactions, and topologic transformations. Useful improvements, as well as extensions to other systems of equations, other applications, higher accuracy orders, and three-dimensional space are explored.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64793/1/sam_3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/64793/2/sam_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/64793/3/sam_2.pd

Computation of flows with moving boundaries and fluid-structure interactions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76296/1/AIAA-1997-1771-882.pd

A simulation technique for 2-D unsteady inviscid flows around arbitrarily moving and deforming bodies of arbitrary geometry

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76229/1/AIAA-1993-3391-356.pd