Parallelization of the Pipelined Thomas Algorithm

In this study the following questions are addressed. Is it possible to improve the parallelization efficiency of the Thomas algorithm? How should the Thomas algorithm be formulated in order to get solved lines that are used as data for other computational tasks while processors are idle? To answer these questions, two-step pipelined algorithms (PAs) are introduced formally. It is shown that the idle processor time is invariant with respect to the order of backward and forward steps in PAs starting from one outermost processor. The advantage of PAs starting from two outermost processors is small. Versions of the pipelined Thomas algorithms considered here fall into the category of PAs. These results show that the parallelization efficiency of the Thomas algorithm cannot be improved directly. However, the processor idle time can be used if some data has been computed by the time processors become idle. To achieve this goal the Immediate Backward pipelined Thomas Algorithm (IB-PTA) is developed in this article. The backward step is computed immediately after the forward step has been completed for the first portion of lines. This enables the completion of the Thomas algorithm for some of these lines before processors become idle. An algorithm for generating a static processor schedule recursively is developed. This schedule is used to switch between forward and backward computations and to control communications between processors. The advantage of the IB-PTA over the basic PTA is the presence of solved lines, which are available for other computations, by the time processors become idle

Conceptual design of a winged hybrid airship

The present study focuses on the sizing and aerodynamic contour design of a two-seater 1000 kg gross take-off mass winged hybrid airship. Unlike the conventional hybrid airships, which stay aloft and takeoff with the help of VTOL propulsion systems, a winged hybrid airship requires a certain speed to takeoff by utilizing lift coming from its aerodynamic surfaces. Heaviness fraction and takeoff ground roll are considered as measure of merit in initial sizing. Based on the design requirement of Malaysian inter-island tourism and transportation of agricultural products, range is set to 450 km and ground roll for take-off about 150 m. For the airship to be heavy enough for ground handling, the ratio of hydrostatic to hydrodynamic lift is set equal to 49:51. Summary of the results to be obtained in early design phase will give a baseline start to study the aerodynamics and stability characteristics of such airships in future

National Aeronautics and

In this study the following questions are addressed. Is it possible to improve the parallelization e#ciency of the Thomas algorithm? How should the Thomas algorithm be formulated in order to get solved lines that are used as data for other computational tasks while processors are idle? To answer these questions, two-step pipelined algorithms (PAs) are introduced formally. It is shown that the idle processor time is invariant with respect to the order of backward and forward steps in PAs starting from one outermost processor. The advantage of PAs starting from two outermost processors is small. Versions of the pipelined Thomas algorithms considered here fall into the category of PAs

National Aeronautics and

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density di#erent from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave results in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically

Optimal Allocation of Boundary Singularities for Stokes Flows about Pairs of Particles

Methods of allocation of singularities for the Method of Fundamental Solutions are proposed, implemented and applied to a Stokes flow about pairs of particles. New local normal and combined Stokeslets allocation methods are proposed to solve Stokes flows using a moderate number of singularities. In the proposed methods the singularities are located at surfaces inside the particles but dissimilar to the particles׳ shapes. Optimization of location of Stokeslets is performed for peanut-shaped and barrel-shaped particles. Convergence of numerical solution as a function of numbers of Stokeslets is evaluated and show substantial reduction in the needed number of Stokeslets compared to the prior methods in which Stokeslets are located at surfaces created similar to the particle shape. Using proposed methods of allocation of Stokeslets, patterns of pressure and velocity vector field near particles are obtained and discussed. The Stokes force exerted by a Stokes flow on the pair of particles is computed at different stages of their collective behavior including separate location of particles in proximity to each other, merging of particles, and re-orientation of cluster along the flow. These results help to determine the least stable location of particles׳ pair for the purpose of their separation off the flow

Aeroacoustics and unsteady pressure load on multiple lifting bodies

This study provides with the computational insight into unsteady far-field and surface pressure generated by vortex-body interaction in lifting flows and flows about multiple bodies in proximity. We address amplification of sound by the mean flow with non-zero circulation, strong influence of vortex profile on the generated sound waves, and very different degree of amplification of sound in lifting flows for localized and non-local vortices. Flows around spinning cylinder and the tandem of two cylinders were taken as simple albeit representative prototypes of flows around multi-element lifting bodies. The unsteady Euler equations are solved in terms of propagating disturbances originated by deforming vortices in the mean flow about rigid bodies. Numerical errors associated with the discretization and boundary conditions were kept small using a high-order scheme with accurate non-reflecting boundary conditions. To model the interaction of vortices with rigid bodies using moderate amount of computational resources, we apply single-grid approach and implement the corresponding transformation of coordinates where it is applicable. The lifting flow about cylinder not only amplifies the sound strength but also shifts the sound directivity. For vortex deforming in the flow around two cylinders, tandem and transverse set-ups of cylinders were investigated. It was found that the vortex trapped between transverse cylinders radiated much stronger noise than the vortex trapped between tandem cylinders. The directivity of sound and maximum of acoustic pressure at cylinder surfaces were found for both cases