Theses and Dissertations
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- All Subjects: Computational Fluid Dynamics
- Creators: Herrmann, Marcus
An interface reconstruction algorithm for the Volume of Fluid (VOF) method is required for two-phase flow problems for advection of phase interface. The primary method for interface reconstruction has been through piecewise linear interface calculation (PLIC) reconstruction. However, while PLIC reconstruction is highly accurate at representing small curvature interfaces by approximating planes across multiple grid cells, accuracy problems arise when the size of the mesh is too coarse to accurately approximate a large curvature without resorting to refining the mesh. An elliptic interface reconstructing algorithm is explored for two-phase flow problems in 2D to determine the viability of a higher-order interface reconstruction algorithm. This requires first developing an area overlap function between an arbitrary triangle and ellipse, which is then extended to calculate the area fraction field of an ellipse within a mesh. Then, the "reverse" problem of elliptic interface reconstruction given an area fraction field is examined. A study is conducted to determine the presence of any local minimums when varying the ellipse parameters. In the future, a multi-dimensional root-finding solver using Newton's Method will be developed to properly reconstruct the elliptic interface given the area fraction field.
The blunt leading-edge wings have less drag because the normal vector of the surface in the front section of the airfoil develops forces at opposed skin friction. The shape of the leading edge, in conjunction with the effect of viscosity, slightly alter the span load; both the magnitude of the lift and the transverse distribution. Another goal in this study is to verify the veracity of wake survey theory; the two different leading-edge shapes reveals the shortcoming of Mclean’s equation which is only applicable to blunt leading-edge wings.
The library is written to let the user determine where to refine and coarsen through custom refinement selector functions for static mesh generation and dynamic mesh refinement, and can handle smooth fields (such as level sets) or localized markers (e.g. density gradients). The library was parallelized with the use of the Zoltan graph-partitioning library, which provides interfaces to both a graph partitioner (PT-Scotch) and a partitioner based on Hilbert space-filling curves. The partitioned adjacency graph, mesh data, and solution variable data is then packed and distributed across all MPI ranks in the simulation, which then regenerate the mesh, generate domain decomposition ghost cells, and create communication caches.
Scalability runs were performed using a Leveque wave propagation scheme for solving the Euler equations. The results of simulations on up to 1536 cores indicate that the parallel performance is highly dependent on the graph partitioner being used, and differences between the partitioners were analyzed. FARCOM is found to have better performance if each MPI rank has more than 60,000 cells.