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A conservative overlap method for multi-block parallelization of compact finite-volume schemes. (English) Zbl 1390.76407
Summary: A conservative approach for MPI-based parallelization of tridiagonal compact schemes is developed in the context of multi-block finite-volume methods. For each block, an enlarged linear system is solved by overlapping a certain number of neighbour cells from adjacent sub-domains. The values at block-to-block boundary faces are evaluated by a high-order centered approximation formula. Unlike previous methods, conservation is retained by properly re-computing the common interface value between two neighbouring blocks. Numerical tests show that parallelization artifacts decrease significantly as the number of overlapping cells is increased, at some expense of parallel efficiency. A reasonable trade-off between accuracy and performances is discussed in the paper with reference to both the spectral properties of the method and the results of fully turbulent numerical simulations.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
76Fxx Turbulence
Software:
incompact3d; SPIKE
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[1] Lele, S. K., Compact finite difference schemes with spectral-like resolution, J Comput Phys, 103, 16-42, (1992) · Zbl 0759.65006
[2] Coppola, G.; Meola, C., Generalization of the spline interpolation based on the principle of the compact schemes, J Sci Comput, 17, 747-760, (2002)
[3] Laizet, S.; Li, N., Incompact3d: a powerful tool to tackle turbulence problems with up to O(10^5) computational cores, Int J Numer Meth Fluids, 67, 1735-1757, (2011) · Zbl 1419.76481
[4] 2Decomp & FFT. http://www.2decomp.org/.
[5] FFTW. http://www.fftw.org/fftw2_doc/fftw_4.html/.
[6] Cook, A. W.; Cabot, W. H.; Williams, P. L.; Miller, B. J.; de Supinski, B. R.; Yates, R. K., Tera-scalable algorithms for variable-density elliptic hydrodynamics with spectral accuracy, Supercomputing, 2005. Proceedings of the ACM/IEEE SC 2005 conference, 60, (2005), IEEE
[7] Povitsky, A.; Morris, P. J., A higher-order compact method in space and time based on parallel implementation of the Thomas algorithm, J Comput Phys, 161, 1, 182-203, (2000) · Zbl 0959.65102
[8] Sun, X.-H.; Moitra, S., A fast parallel tridiagonal algorithm for a class of CFD applications, 3585, (1996), NASA technical paper
[9] Polizzi, E.; Sameh, A. H., A parallel hybrid banded system solver: the spike algorithm, Parallel Comput, 32, 2, 177-194, (2006)
[10] Ladeinde, F.; Cai, X.; Visbal, M.; Gaitonde, D., Parallel implementation of curvilinear high-order formulas, Int J Comput Fluid D, 17, 6, 467-485, (2003) · Zbl 1161.76527
[11] Situ, Y.; Martha, C. S.; Louis, M. E.; Li, Z.; Sameh, A. H.; Blaisdell, G. A., Petascale large eddy simulation of jet engine noise based on the truncated spike algorithm, Parallel Comput, 40, 9, 496-511, (2014)
[12] Kim, J. W., Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters, J Comput Phys, 241, 168-194, (2013) · Zbl 1349.65738
[13] Colonius, T.; Lele, S. K., Computational aeroacoustics: progress on nonlinear problems of sound generation, Prog Aerosp Sci, 40, 345-416, (2004)
[14] Sengupta, T. K.; Dipankar, A.; Rao, A. K., A new compact scheme for parallel computing using domain decomposition, J Comput Phys, 220, 654-677, (2007) · Zbl 1370.76072
[15] Gaitonde, D. V.; Visbal, M. R., Padé-type higher-order boundary filters for the Navier-Stokes equations, AIAA J, 38, 2103-2112, (2000)
[16] Kim, J. W.; Sandberg, R. D., Efficient parallel computing with a compact finite difference scheme, Comp Fluids, 58, 70-87, (2012) · Zbl 1365.65196
[17] Zhang, X.; Blaisdell, G. A.; Lyrintzis, A. S., High-order compact schemes with filters on multi-block domains, J Sci Comput, 21, 3, 321-339, (2004) · Zbl 1069.76043
[18] Chao, J.; Haselbacher, A.; Balachandar, S., A massively parallel multi-block hybrid compact-WENO scheme for compressible flows, J Comput Phys, 228, 19, 7473-7491, (2009) · Zbl 1172.76033
[19] Ferziger, J. H.; Perić, M., Computational methods for fluid dynamics, (2013), Springer · Zbl 0869.76003
[20] Lacor, C.; Smirnov, S.; Baelmans, M., A finite volume formulation of compact central schemes on arbitrary structured grids, J Comput Phys, 198, 535-566, (2004) · Zbl 1051.65086
[21] Fosso, P.; Deniau, H.; Sicot, F.; Sagaut, P., Curvilinear finite-volume schemes using high-order compact interpolation, J Comput Phys, 229, 5090-5122, (2010) · Zbl 1346.76081
[22] Gamet, L.; Ducros, F.; Nicoud, F.; Poinsot, T., Compact finite difference schemes on non-uniform meshes. application to direct numerical simulations of compressible flows, Int J Numer Methods Fluids, 29, 2, 159-191, (1999) · Zbl 0939.76060
[23] Ducros, F.; Laporte, F.; Soulères, T.; Guinot, V.; Moinat, P.; Caruelle, B., High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows, J Comput Phys, 161, 114-139, (2000) · Zbl 0972.76066
[24] Capuano, F.; Coppola, G.; Balarac, G.; de Luca, L., Energy preserving turbulent simulations at a reduced computational cost, J Comput Phys, 298, 480-494, (2015) · Zbl 1349.76051
[25] Hu, F.; Hussaini, M.; Manthey, J., Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics, J Comput Phys, 124, 177-191, (1996) · Zbl 0849.76046
[26] Capuano, F.; Coppola, G.; de Luca, L., An efficient time advancing strategy for energy-preserving simulations, J Comput Phys, 295, 209-229, (2015) · Zbl 1349.65394
[27] Capuano, F.; Coppola, G.; Rández, L.; de Luca, L., Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties, J Comput Phys, 328, 86-94, (2017)
[28] Nabben, R., Decay rates of the inverse of nonsymmetric tridiagonal and band matrices, SIAM J Matrix Anal Appl, 20, 820-837, (1999) · Zbl 0931.15001
[29] McNally, J. M.; Garey, L. E.; Shaw, R. E., A communication-less parallel algorithm for tridiagonal Toeplitz systems, J Comput Appl Math, 212, 260-271, (2008) · Zbl 1132.65019
[30] Kobayashi, M. H., On a class of Padé finite volume methods, J Comput Phys, 156, 1, 137-180, (1999) · Zbl 0940.65092
[31] Shu, C.-W., Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced numerical approximation of nonlinear hyperbolic equations, 325-432, (1998), Springer · Zbl 0927.65111
[32] Sengupta, T. K.; Ganeriwal, G.; De, S., Analysis of central and upwind compact schemes, J Comput Phys, 192, 2, 677-694, (2003) · Zbl 1038.65082
[33] Capuano, F.; Mastellone, A.; Di Benedetto, S.; Cutrone, L.; Schettino, A., Preliminary developments towards a high-order and efficient LES code for propulsion applications, Proceedings of the jointly organized WCCM XI-ECCM V-ECFD VI, 7569-7580, (2014)
[34] Wang, Z. J.; Fidkowski, K.; Abgrall, R.; Bassi, F.; Caraeni, D.; Cary, A., High-order CFD methods: current status and perspective, Int J Numer Methods Fluids, 72, 8, 811-845, (2013)
[35] van Rees, W. M.; Leonard, A.; Pullin, D.; Koumoutsakos, P., A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers, J Comput Phys, 230, 2794-2805, (2011) · Zbl 1316.76066
[36] Galileo. http://www.hpc.cineca.it/hardware/galileo.
[37] Marconi. http://www.hpc.cineca.it/hardware/marconi.
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