Newton-Krylov-Schwarz methods for aerodynamics problems : compressible and incompressible flows on unstructured grids.

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We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for flow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in different physical regimes, and on comparing the performance of currently important computational platforms. Multiple-scale problems should be marched out at desired accuracy limits, and not held hostage to often more stringent explicit stability limits. In the context of inviscid aerodynamics, this ... continued below

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10 p.

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Kaushik, D. K.; Keyes, D. E. & Smith, B. F. February 24, 1999.

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We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for flow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in different physical regimes, and on comparing the performance of currently important computational platforms. Multiple-scale problems should be marched out at desired accuracy limits, and not held hostage to often more stringent explicit stability limits. In the context of inviscid aerodynamics, this means evolving transient computations on the scale of the convective transit time, rather than the acoustic transit time, or solving steady-state problems with local CFL numbers approaching infinity. Whether time-accurate or steady, we employ Newton's method on each (pseudo-) timestep. The coupling of analysis with design in aerodynamic practice is another motivation for implicitness. Design processes that make use of sensitivity derivatives and the Hessian matrix require operations with the Jacobian matrix of the state constraints (i.e., of the governing PDE system); if the Jacobian is available for design, it may be employed with advantage in a nonlinearly implicit analysis, as well.

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10 p.

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OSTI as DE00012411

Medium: P; Size: 10 pages

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  • 11th International Conference on Domain Decomposition Methods, London (GB), 07/20/1998--07/24/1998

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  • Report No.: ANL/MCS/CP-98468
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 12411
  • Archival Resource Key: ark:/67531/metadc619762

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  • February 24, 1999

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  • June 16, 2015, 7:43 a.m.

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  • April 6, 2017, 6:48 p.m.

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Kaushik, D. K.; Keyes, D. E. & Smith, B. F. Newton-Krylov-Schwarz methods for aerodynamics problems : compressible and incompressible flows on unstructured grids., article, February 24, 1999; Illinois. (digital.library.unt.edu/ark:/67531/metadc619762/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.