Parallel direct numerical simulation of wake vortex detection using monostatic and bistatic radio acoustic sounding systems.

摘要

A parallel two-dimensional code is developed in this thesis to numerically simulate wake vortex detection using a Radio Acoustic Sounding System (RASS). The Maxwell equations for media with non-uniform permittivity and the linearized Euler equations for media with non-uniform mean flow are the main framework for the simulations. The code is written in Fortran 90 with the Message Passing Interface (MPI) for parallel implementation.; The main difficulty encountered with a time accurate simulation of a RASS is the number of samples required to resolve the Doppler shift in the scattered electromagnetic signal. Even for a 1D simulation with a typical scatterer size, the CPU time required to run the code is far beyond currently available computer resources. Two solutions that overcome this problem are described. In the first the actual electromagnetic wave propagation speed is replaced with a much lower value. This allows an explicit, time accurate numerical scheme to be used. In the second the governing differential equations are recast in order to remove the carrier frequency and solve only for the frequency shift using an implicit scheme with large time steps. The numerical stability characteristics of the resulting discretized equation with complex coefficients are examined.; A number of cases for both the monostatic and bistatic configurations are considered. First, a uniform mean flow is considered and the RASS simulation is performed for two different types of incident acoustic field, namely a short single frequency acoustic pulse and a continuous broadband acoustic source. Both the explicit and implicit schemes are examined and the mean flow velocity is determined from the spectrum of the backscattered electromagnetic signal with very good accuracy. Second, the Taylor and Oseen vortex models are considered and their velocity field along the incident electromagnetic beam is retrieved. The Abel transform is then applied to the velocity profiles determined by both explicit and implicit schemes, and the radial variation of the wake vortex velocity is reconstructed. The effect of the transmitter beam width on the results is also examined.; The parallel performance of the simulations on several platforms is investigated. It is found that the code is nearly perfectly scalable on the tested platforms and for the number of processors considered.