Simulation of transonic flows using quad-core OpenMP Euler, flux modified transonic small disturbance, and Fluent codes

Abstract

This article investigates what performance can be achieved when executing an aerodynamic code on a quad-core based personal computer with an OpenMP compiler in a Windows environment. Euler equations are solved in two dimensions for simplicity, to predict flow field around an aerofoil on an O-type boundary fitted structured grid. The grid is generated by solving a system of Poisson's equations utilising an efficient method of false transients, coupled with an approximate factorisation technique and variable time steps cycling process. Comparison between the OpenMP Euler, flux modified transonic small disturbance and Fluent results for transonic flow fields, with shock waves, around a NACA0012 aerofoil is presented. References Bailey, D., Barszcz, E., Barton, J., Browning, D., Carter, R., Dagum, L., Fatoohi, R., Fineberg, S., Frederickson, P., Lasinski, T., Schreiber, R., Simon, H., Venkatakrishnan, V., and Weeratunga, S., The NAS Parallel Benchmarks, Contractor Report 203186, NASA, USA, 1994. Engquist, B., and Osher, S., Stable and Entropy Satisfying Approximations for Transonic Flow Calculations, Mathematics of Computation, 34, 149, January 1980, pp. 45--75. Gear, J., Ly, E., and Phillips, N. J. T., A Time Marching, Type-Dependent, Finite Difference Algorithm for the Modified Transonic Small Disturbance Equation, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), ICAS and AIAA, Melbourne, Australia, 1998, Paper A98-31513. Hirsch, C., Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows, Volume 2, John Wiley and Sons, Great Britain, 1992. Jin, H., Frumkin, M., and Yan, J., The OpenMP Implementation of NAS Parallel Benchmarks and its Performance, Technical Report NAS-99-011, NASA, Moffett Field, USA, 1999. Liu, Y., and Vinokur, M., Nonequilibrium Flow Computations 1: An Analysis of Numerical Formulations of Conservation Laws, Contractor Report 177489, NASA, California, USA, 1988. Lock, R. C., Test Cases for Numerical Methods in Two-Dimensional Transonic Flows, Report Number 575, AGARD, 1970. Ly, E., Improved Approximate Factorisation Algorithm for the Steady Subsonic and Transonic Flow over an Aircraft Wing, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), ICAS and AIAA, Melbourne, Australia, 1998, Paper Number A98-31699. Ly, E., and Nakamichi, J., Time-Linearised Transonic Computations Including Entropy, Vorticity and Shock Wave Motion Effects, The Aeronautical Journal, November 2003, pp. 687--695. Ly, E., and Norrison, D., Automatic Elliptic Grid Generation by an Approximate Factorisation Algorithm, ANZIAM Journal, 48 (CTAC2006), pp. C188--C202, July 2007. Murman, E., Analysis of Embedded Shock Waves Calculated by Relaxation Methods, AIAA Journal, 12, 5, May 1974, pp. 626--633. Pulliam, T., Kutler, P., and Rossow, V., Harvard Lomax: His Quiet Legacy to Computational Fluid Dynamics, 14th AIAA Computational Fluid Dynamics Conference, Norfolk, VA, June 1999. Steger, J.L., and Warming, R. F., Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite Difference Methods, Technical Memorandum TM-78605, NASA, California, USA, 1979. Van Leer, B., Flux-Vector Splitting for the Euler Equations, Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen, West Germany, 1982.