Abstract
A numerical algorithm for simulating gas dynamics in rotor–stator systems based on sliding meshes and edge-based schemes is described. The paper pays particular attention to the multilevel MPI + OpenMP parallelization for cluster systems. Parallel efficiency is demonstrated on up to 1400 cores as well as on Intel Xeon Phi accelerators. The scheme is verified by solving a linear acoustic problem. The robustness of the algorithm is demonstrated on the simulation of a model fan.
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REFERENCES
I. V. Abalakin, V. A. Anikin, P. A. Bakhvalov, V. G. Bobkov, and T. K. Kozubskaya, “Numerical simulation of aerodynamic and acoustic characteristics of a ducted rotor,” Math. Models Comput. Simul. 8 (3), 309–324 (2016).
B. Koobus and C. Farhat, “Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes,” Comput. Methods Appl. Mech. Eng. 170 (1–2), 103–129 (1999).
T. J. Barth, “Numerical aspects of computing high Reynolds number flows on unstructured meshes,” AIAA Paper No. 91-0721 (1991).
A. Katz and V. Sankaran, “An efficient correction method to obtain a formally third-order accurate flow solver for node-centered unstructured grids,” J. Sci. Comput. 51 (2), 375–393 (2012).
B. B. Pincock and A. Katz, “High-order flux correction for viscous flows on arbitrary unstructured grids,” J. Sci. Comput. 61 (2), 454–476 (2014).
P. A. Bakhvalov and T. K. Kozubskaya, “Modification of Flux Correction method for accuracy improvement on unsteady problems,” J. Comput. Phys. 338, 199–216 (2017).
C. Debiez and A. Dervieux, “Mixed-element-volume MUSCL methods with weak viscosity for steady and unsteady flow calculations,” Comput. Fluids 29 (1), 89–118 (2000).
I. Abalakin, P. Bakhvalov, and T. Kozubskaya, “Edge-based reconstruction schemes for unstructured tetrahedral meshes,” Int. J. Numer. Methods Fluids 81 (6), 331–356 (2016).
P. Bakhvalov and T. Kozubskaya, “EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes,” Comput. Fluids 157, 312–324 (2017).
M. A. Burgos, J. Contreras, and R. Corral, “Efficient edge-based rotor/stator interaction method,” AIAA J. 49 (1), 19–31 (2011).
V. A. Titarev, G. A. Faranosov, S. A. Chernyshev, and A. S. Batrakov, “Numerical modeling of the influence of the relative positions of a propeller and pylon on turboprop aircraft noise,” Acoust. Phys. 64 (6), 760–773 (2018).
T. J. Barth, “A 3-D upwind Euler solver for unstructured meshes,” AIAA Paper No 91-1548 (1991).
P. A. Bakhvalov and T. K. Kozubskaya, “Construction of edge-based 1-exact schemes for solving the Euler equations on hybrid unstructured meshes,” Comput. Math. Math. Phys. 57 (4), 680–697 (2017).
P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,” J. Comput. Phys. 43 (2), 357–372 (1981).
E. Turkel, “Preconditioning techniques in computational fluid dynamics,” Annu. Rev. Fluid Mech. 31, 385–416 (1999).
P. A. Bakhvalov, “Flow simulation in rotor–stator systems with axisymmetric stator using edge-based schemes,” KIAM Preprint No. 124 (Keldysh Inst. Appl. Math., Moscow, 2018) [in Russian]. https://doi.org/10.20948/prepr-2018-124
I. V. Abalakin, P. A. Bakhvalov, A. V. Gorobets, A. P. Duben, and T. K. Kozubskaia, “Parallel program complex NOISEtte for large-scale computations of aerodynamics and aeroacoustics problems,” Vychisl. Metody Program. 13 (3), 110–125 (2012).
A. Gorobets, “Parallel algorithm of the NOISEtte Code for CFD and CAA simulations,” Lobachevskii J. Math. 39 (4), 524–532 (2018). https://doi.org/10.1134/S1995080218040078
H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13 (2), 631–644 (1992).
P. A. Bakhvalov and A. V. Gorobets, “On effective parallel implementation of vertex-centered schemes on sliding meshes,” KIAM Preprint No. 277 (Keldysh Inst. Appl. Math., Moscow, 2018) [in Russian]. https://doi.org/10.20948/prepr-2018-277
ACKNOWLEDGMENTS
This study is carried out using the equipment of the resource sharing center Complex for Simulation and Data Processing for Mega-Science Facilities at Kurchatov Institute (http://ckp.nrcki.ru/) and of the resource sharing center at Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (https://ckp.kiam.ru/).
Funding
This study is supported by the Russian Foundation for Basic Research (project no. 18-01-00445; development of the numerical method) and by the Council for Grants of the President of Russia (project MD-5968.2018.1, reduction in the intensity of computational resources).
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Translated by E. Oborin
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Abalakin, I.V., Bakhvalov, P.A., Bobkov, V.G. et al. Parallel Algorithm for Flow Simulation in Rotor–Stator Systems Based on Edge-Based Schemes. Math Models Comput Simul 13, 172–180 (2021). https://doi.org/10.1134/S2070048221010026
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DOI: https://doi.org/10.1134/S2070048221010026