An adaptive three-dimensional Cartesian approach for the parallel computation of inviscid flow about static and dynamic configurations.

An adaptive three-dimensional Cartesian approach for the parallel computation of compressible flow about static and dynamic configurations has been developed and validated. This is a further step towards a goal that remains elusive for CFD codes: the ability to model complex dynamic-geometry problems in a quick and automated manner. The underlying flow-solution method solves the three-dimensional Euler equations using a MUSCL-type finite-volume approach to achieve higher-order spatial accuracy. The flow solution, either steady or unsteady, is advanced in time via a two-stage time-stepping scheme. This basic solution method has been incorporated into a parallel block-adaptive Cartesian framework, using a block-octtree data structure to represent varying spatial resolution, and to compute flow solutions in parallel. The ability to represent static geometric configurations has been introduced by cutting a geometric configuration out of a background block-adaptive Cartesian grid, then solving for the flow on the resulting volume grid. This approach has been extended for dynamic geometric configurations: components of a given configuration were permitted to independently move, according to prescribed rigid-body motion. Two flow-solver difficulties arise as a result of introducing static and dynamic configurations: small time steps; and the disappearance/appearance of cell volume during a time integration step. Both of these problems have been remedied through cell merging. The concept of cell merging and its implementation within the parallel block-adaptive method is described. While the parallelization of certain grid-generation and cell-cutting routines resulted from this work, the most significant contribution was developing the novel cell-merging paradigm that was incorporated into the parallel block-adaptive framework. Lastly, example simulations both to validate the developed method and to demonstrate its full capabilities have been carried out. A simple, steady reflected shock case is presented to validate the basic flow solver. A steady diamond-airfoil case is presented to validate the cell-cutting approach for static geometries. A shock impinging on two cylinders is presented to validate the unsteady flow-solution algorithm. A dynamic-geometry case, directly analogous to the steady diamond-airfoil case, is presented to validate the dynamic cell-merging algorithm. A steady finite-wing calculation, presented to validate the three-dimensional flow solver and static-geometry cell cutting, is presented. The final case in the dissertation, demonstrates the full capabilities of the code developed in this work: it is three-dimensional and involves a dynamic geometry with bodies moving relative to each other.PhDAerospace engineeringApplied SciencesComputer sciencePlasma physicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124078/2/3121947.pd