Finite element multigrid solution of Euler flows past installed aero- engines. (English) Zbl 0771.76041

Summary: A finite element based procedure for the solution of the compressible Euler equations on unstructured tetrahedral grids is described. The spatial discretization is accomplished by means of an approximate variational formulation, with the explicit addition of a matrix form of artificial viscosity. The solution is advanced in time by means of an explicit multi-stage time stepping procedure. The method is implemented in terms of an edge based representation for the tetrahedral grid. The solution procedure is accelerated by use of a fully unstructured multigrid algorithm. The approach is applied to the simulation of the flow past an installed aero-engine nacelle, at three different free stream conditions. Comparison is made between the numerical predictions and experimental pressure observations.


76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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[1] Baker, T. J. (1990): Unstructured mesh generation by a generalised Delaunay algorithm. In: AGARD Conference Proceedings No. 464, Applications of Mesh Generation to Complex 3-D Configurations. AGARD, Neuilly Sur Seine. 20.1-20.10
[2] Barth, T. J.; Jespersen, D. C. (1989): The design and application of upwind schemes on unstructured meshes. AIAA Paper 89-0366
[3] Barth, T. J. (1991): Numerical aspects of computing viscous high Reynolds number flows on unstructured meshes. AIAA Paper 91-0721
[4] Bonet, J.; Peraire, J. (1991): An alternate digital tree algorithm for geometric searching and intersection problems. Int. J. Num. Meth. Engng. 31, 1-17 · Zbl 0825.73958
[5] Formaggia, L.; Peraire, J.; Morgan, K.; Peiró, J. (1988): Implementation of a 3D explicit Euler solver on a CRAY computer. In: Proceedings of the 4th International Symposium on Science and Engineering on CRAY Supercomputers. Minneapolis, 45-65
[6] Giles, M. (1987): Energy stability analysis of multi-step methods on unstructured meshes. MIT CFD Laboratory report CFDL-TR-87-1. Cambridge, Massachusetts
[7] Jameson, A.; Schmidt, W.; Turkel, E. (1981): Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping. AIAA paper 81-1259
[8] Jameson, A. (1984): Transonic flow calculations. Princeton University Report MAE 1751 · Zbl 0553.76049
[9] Jameson, A.; Baker, T. J.; Weatherill, N. P. (1986): Calculation of inviscid transonic flow over a complete aircraft. AIAA paper 86-0103
[10] Leclercq, M.-P.; Periaux, J.; Stoufflet, B. (1989): Multigrid methods with unstructured meshes. In: Proceedings of the 7th International Conference on Finite Elements in Flow Problems. Huntsville, Alabama. 1113-1118
[11] Löhner, R.; Morgan, K. (1987): Unstructured multigrid methods for elliptic problems. Int. J. Num. Meth. Engng. 24, 101-115 · Zbl 0624.65103
[12] Mavriplis, D. J. (1988): Multigrid solution of the two dimensional Euler equations on unstructured triangular meshes. AIAA J. 26, 824-831 · Zbl 0667.76088
[13] Mavriplis, D. J. (1991): Three dimensional unstructured multigrid for the Euler equations. AIAA Paper 91-1549
[14] Morgan, K.; Peraire, J.; Peiró, J. (1992): Unstructured grid methods for compressible flows. In: AGARD Report No. 787, Special Course on Unstructured Grid Methods for Advection Dominated Flows. AGARD, Neuilly Sur Seine. 5.1-5.39
[15] Numerical Aerodynamic Simulation Program Technical Summaries (1992): March 1990?February 1991, NASA Ames Research Center
[16] Peraire, J.; Morgan, K.; Peiró, J.; Zienkiewicz, O. C. (1987): An adaptive finite element method for high speed flows. AIAA paper 87-0558
[17] Peraire, J.; Morgan, K.; Peiró, J. (1990): Unstructured finite element mesh generation and adaptive procedures for CFD. In: AGARD Conference Proceedings No. 464, Applications of Mesh Generation to Complex 3D Configurations. AGARD, Neuilly Sur Seine. 18.1-18.12
[18] Peraire, J.; Morgan, K.; Vahdati, M.; Peiró, J. (1992): The construction and behaviour of some unstructured grid algorithms for compressible flows. In: Baines, M. J.; Morton, K. W. (ed): Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics. Oxford University Press (to appear) · Zbl 0801.76047
[19] Peraire, J.; Morgan, K.; Peiró, J. (1992): A finite element multigrid solver for the Euler equations. AIAA paper 92-0449
[20] Perez, E. (1985): Finite element and multigrid solution of the two dimensional Euler equations on a non-structured mesh. INRIA report no. 442, INRIA, Paris
[21] Pugh, G.; Harris, A. (1981): Establishment of an experimental technique to provide accurate measurement of the installed drag of close-coupled civil nacelle/airframe configurations using a full span model with turbine powered engine simulators. AGARD Conference Proceedings No. 301. AGARD, Neuilly Sur Seine
[22] Roe, P. (1981): Approximate Riemann solvers, parameter vectors and difference schemes. J Comput. Phys. 43, 357-372 · Zbl 0474.65066
[23] Smith, R. E. (ed) (1992): Software Systems for Surface Modeling and Grid Generation, NASA Conference Publication 3143
[24] Swanson, R. C.; Turkel, E. (1990): On central difference and upwind schemes. ICASE Report No. 90-44. NASA Langley Research Center · Zbl 0757.76044
[25] Zienkiewicz, O. C.; Morgan, K. (1983): Finite elements and approximation. New York: Wiley · Zbl 0582.65068
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