Abstract
The time-dependent formulation is most often used to compute steady state solutions to the Euler equations. There are several mechanisms that drive the solution to a steady state. Here we shall concentrate on the dissipation effect due to the boundary conditions, and not to the effect of artificial viscosity. Therefore we shall study hyperbolic partial differential equations where the boundary effects are dominant. The results are also valid for more general classes of differential equations of essentially hyperbolic character, as for example the Navier-Stokes equations for high Reynolds numbers. The study is mathematical, much of it repeated from Ref. 1.
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References
Engqvist, B., Gustafsson, B.: “Steady State Computations for Wave Propagation Problems”. Math. Comp., Vol. 49, No. 179, July 1987, pp. 39–64.
Giles, M.B.: “Eigenmode Analysis of Unsteady One-Dimensional Euler Equations”. ICASE Report No. 83–47, 1983.
Eriksson, L.E., Rizzi, A.: “ Computer-Aided Analysis of the Convergence to Steady State of Discrete Approximations to the Euler Equations”. J. Comput. Phys., Vol. 57, 1985, pp. 90–128.
Ferm, L., Gustafsson, B.: “A Down-Stream Boundary Procedure for the Euler Equations”. Comput. & Fluids. Vol. 10, 1982, pp. 261–276.
Morawetz, C.S.: “The Decay of Solutions to the Exterior Initial-Boundary Value Problem for the Wave Equation”. C.mm. Pure Appl. Math., Vol. 14, 1961, pp. 561–568.
Morawetz, C.S.: “Decay of Solutions of the Exterior Problem for the Wave Equation”. C.mm. Pure Appl. Math., Vol. 28, 1975, pp. 229–264.
Morawetz, C.S., Ralston, J.V., Strauss, W.A.: “Decay of Solutions of the Wave Equation Outside Nontrapping Obstacles”. Comm. Pure Appl. Math., Vol. 30, 1977, pp. 447–508.
Jameson, A,: “Transonic Flow Calculations for Aircraft”. Lecture Notes in Mathematics, Vol. 1127, Numerical Methods in Fluid Dynamics, F. Brezzi (ed.), Springer Verlag, 1985, pp. 156–242.
MacCormack, R.W.: “A Numerical Method for Solving the Equations of Compressible Viscous Flows”. AIAA-Paper 81–110, 1981.
Lerat, A., Sidés, J.: “A New Finite Volume Method for the Euler Equations with Applications to Transonic Flows”. Proc. IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, Reading, 1981, P.L. Roe (ed.), Academic Press, New York, 1982, pp. 245–288.
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© 1992 Springer Fachmedien Wiesbaden
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Eberle, A., Rizzi, A., Hirschel, E.H. (1992). Convergence to Steady State. In: Numerical Solutions of the Euler Equations for Steady Flow Problems. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06831-0_7
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DOI: https://doi.org/10.1007/978-3-663-06831-0_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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