Data-parallel total variation diminishing method for sonic boom calculations

Abstract

Sonic boom predictions are shown for the near and midfield and comparisons are made with experimental data. The computations are performed on the Thinking Machines' CM-5 massively parallel supercomputer to utilize its large available memory and high floating point performance. A second-order-accurate total variation diminishing scheme is used to solve the Euler equations in the computations. Additionally, a recently developed implicit method, based on the LU-SGS algorithm, is used to speed the convergence and accuracy of the steady- state computations. The method is shown to work well on near- and midfield sonic boom predictions for several test cases. HE projected use of the high speed civil transport (HSCT) has drawn attention to the problems associated with the noise due to sonic booms.1 An accurate and efficient sonic boom prediction methodology is needed for the assessment of various proposed HSCT configurations. One such method that utilizes the power of massively parallel supercomputers is presented here. A review of current sonic boom prediction methods is given by Plotkin.2 Many of these methods are based on the modified linear analysis of Whitham 3 and Walkden.4 Other methods have been developed based on a modified method of char- acteristics that approximately account for the effects of three- dimensional flows. Experimental and analytical studies have shown that these methods lose effectiveness as freestream Mach number approaches 3. In high Mach number regions there are strong shock waves with significant entropy gen- eration. The linear-based methods neglect these production terms.5 A modified method of characteristi cs has been de- veloped that can account for these terms,6 but it requires nonlinear near-field initial data that is difficult to obtain com- putationally or experimentall y. Several authors have developed prediction methods based on near-field solutions of the Euler or Navier-Stokes equa- tions.7-8 Most of these methods involve marching in one spatial dimension with an implicit Euler scheme or a parabolized Navier-Stokes (PNS) algorithm. These solutions are used in conjuction with Whitham's F-function to evaluate the far-field pressure signature. The existing prediction methods are un- attractive for several reasons. First, additional accuracy in the marching direction greatly increases the computational time. Also, they do not employ methods designed to resolve shock waves effectively. Finally, they are not easily implemented on massively parallel supercomputers. Accurate shock resolution is needed in the computational fluid dynamic (CFD) methods to determine the far-field pres- sure signature effectively. Since the prediction methods are dependent on shock resolution it is desirable to use a com- putational method that is designed to capture shock waves. The total variation diminishing (TVD) schemes developed by Harten,9 Yee,10 and others are well suited for this purpose. In this study a second-order-accurate TVD scheme is used to determine the pressure field about several models. These so- lutions are then compared with experiment.