Abstract
A space-time domain decomposition algorithm for the compressible Navier–Stokes problem has been designed, with the aim of implementing it in three dimensions, in an industrial code. The system is discretised with a second order implicit scheme in time and Finite Volumes Method in space. To achieve full speedup performance, a Schwarz Waveform Relaxation method coupled with a Newton procedure is used, as it allows local space and time stepping. The performances of different parallelisation strategies (using OpenMP, MPI and GPUs) are compared in difficult configurations.
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References
X.-C. Cai, D.E. Keyes, Nonlinearly preconditioned inexact Newton algorithms. SIAM 24(1),183–200 (2002)
T. Colonius, S.K. Lele, P. Moin, Sound generation in a mixing layer. J. Fluid Mech. 330,375–409 (1997)
CUDA (2015), http://www.nvidia.com/object/cuda_home_new.html
M.J. Gander, Overlapping Schwarz waveform relaxation for parabolic problems, in DD10 Proceedings, vol. 218 (1998), pp. 425–431
M.J. Gander, A.M. Stuart, Space-time continuous analysis of waveform relaxation for the heat equations. SIAM 19(6), 2014–2031 (1998)
F. Haeberlein, Time-space domain decomposition methods for reactive transport. Ph.D. thesis, University Paris 13, 2011
F. Haeberlein, L. Halpern, Optimized Schwarz waveform relaxation for nonlinear systems of parabolic type, in DD21 Proceedings (2012)
L. Halpern, J. Ryan, M. Borrel, Domain decomposition vs. overset Chimera grid approaches for coupling CFD and CAA, in ICCFD7 (2012)
R. Jeltsch, B. Pohl, Waveform relaxation with overlapping splittings. SIAM 16(1), 40–49 (1995)
D.E. Keyes, Domain decomposition in the mainstream of computational science, in DD14 Proceedings (2002)
D.A. Knoll, D.E. Keyes, Jacobian-free Newton–Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193(2), 357–397 (2004)
E. Lelarasmee, A.E. Ruehli, A.L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE 1(3), 131–145 (1982)
M.-S. Liou, A sequel to AUSM, part II: AUSM+-up for all speeds. J. Comput. Phys. 214(1), 137–170 (2006)
B. Ong, S. High, F. Kwok, Pipeline Schwarz waveform relaxation, in 22nd DDM Conference (2013, submitted)
H.C. Yee, N.D. Sandham, M.J. Djomehri, Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150(1), 199–238 (1999)
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Ciobanu, O., Halpern, L., Juvigny, X., Ryan, J. (2016). Overlapping Domain Decomposition Applied to the Navier–Stokes Equations. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_47
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DOI: https://doi.org/10.1007/978-3-319-18827-0_47
Publisher Name: Springer, Cham
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