Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm

We study the convergence characteristics of two algebraic kernels used in vortex calculations: the Rosenhead–Moore kernel, which is a low-order kernel, and the Winckelmans–Leonard kernel, which is a high-order kernel. To facilitate the study, a method of evaluating particle-cluster interactions is introduced for the Winckelmans–Leonard kernel. The method is based on Taylor series expansion in Cartesian coordinates, as initially proposed by Lindsay and Krasny [J. Comput. Phys., 172 (2001), pp. 879–907] for the Rosenhead–Moore kernel. A recurrence relation for the Taylor coefficients of the Winckelmans–Leonard kernel is derived by separating the kernel into two parts, and an error estimate is obtained to ensure adaptive error control. The recurrence relation is incorporated into a tree-code to evaluate vorticity-induced velocity. Next, comparison of convergence is made while utilizing the tree-code. Both algebraic kernels lead to convergence, but the Winckelmans–Leonard kernel exhibits a superior convergence rate. The combined desingularization and discretization error from the Winckelmans–Leonard kernel is an order of magnitude smaller than that from the Rosenhead–Moore kernel at a typical resolution. Simulations of vortex rings are performed using the two algebraic kernels in order to compare their performance in a practical setting. In particular, numerical simulations of the side-by-side collision of two identical vortex rings suggest that the three-dimensional evolution of vorticity at finite resolution can be greatly affected by the choice of the kernel. We find that the Winckelmans–Leonard kernel is able to perform the same task with a much smaller number of vortex elements than the Rosenhead–Moore kernel, greatly reducing the overall computational cost.U.S. Department of Energy, Mathematical, Information, and Computational Sciences (MICS) program (DE-FG02-98ER25355

Hybrid Eulerian/Lagrangian 3D methods for high Reynolds number reactive flows

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 171-177).Research in advanced combustion modeling is critical to developing control strategies for optimized propulsion systems, especially with regard to stability, emissions, and power density. Examining combustion dynamics and control using numerical simulations, however, presents several challenges, given the multiscale and multiphysics nature of the underlying flows. This thesis presents progresses in combustion modeling for the numerical simulation of turbulent reactive jet flows through the design of a hybrid Eulerian/Lagrangian and massively parallel 3D numerical simulation tool. The adaptivity of the resulting software yields truly fast and accurate simulations, and a better understanding of the simulated combustion processes. The transverse jet vorticity dynamics at high Reynolds numbers are first described, and more specifically the unsteady interactions between the wall boundary layer and the jet. We then present actuation strategies that manipulate the jet penetration and spread via simple nozzle-edge perturbations. Finally, the adaptive Eulerian/Lagrangian code is used to provide a detailed understanding of flame anchoring mechanisms in transverse reactive jets.by Fabrice Schlegel.Ph.D