Abstract:
In this paper, 1-exact vertex-centered finite-volume schemes with an edge-based approximation of fluxes are constructed for numerically solving hyperbolic problems on hybrid unstructured meshes. The 1-exactness property is ensured by introducing a new type of control volumes, which are called semitransparent cells. The features of a parallel algorithm implementing the computations using semitransparent cells on modern supercomputers are described. The results of solving linear and nonlinear test problems are given.
Key words:
control volumes, vertex-centered schemes, edge-based approximation of fluxes, hybrid unstructured meshes.
Citation:
P. A. Bakhvalov, T. K. Kozubskaya, “Construction of edge-based 1-exact schemes for solving the Euler equations on hybrid unstructured meshes”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 682–701; Comput. Math. Math. Phys., 57:4 (2017), 680–697
This publication is cited in the following 29 articles:
Alexey Duben, Andrey Gorobets, “Scale-resolving simulation of a low-pressure turbine on hybrid supercomputers”, Computers & Fluids, 265 (2023), 105984
Pavel Bakhvalov, Mikhail Surnachev, “On the Order of Accuracy of Edge-Based Schemes: a Peterson-Type Counter-Example”, Commun. Appl. Math. Comput., 2023
Gorobets A., Bakhvalov P., “Heterogeneous Cpu Plus Gpu Parallelization For High-Accuracy Scale-Resolving Simulations of Compressible Turbulent Flows on Hybrid Supercomputers”, Comput. Phys. Commun., 271 (2022), 108231
Bakhvalov P.A., Surnachev M.D., “Method of Averaged Element Splittings For Diffusion Terms Discretization in Vertex-Centered Framework”, J. Comput. Phys., 450 (2022), 110819
Pavel Bakhvalov, Tatiana Kozubskaya, Pavel Rodionov, “EBR schemes with curvilinear reconstructions for hybrid meshes”, Computers & Fluids, 239 (2022), 105352
V. G. Bobkov, V. A. Vershkov, T. K. Kozubskaya, V. O. Tsvetkova, “Method of unstructured mesh deformation to find aerodynamic characteristics of a body at small displacements”, Math. Models Comput. Simul., 13:6 (2021), 986–1001
Vladimir Bobkov, Andrey Gorobets, Tatiana Kozubskaya, Xin Zhang, Siyang Zhong, Communications in Computer and Information Science, 1510, Supercomputing, 2021, 256
I. V. Abalakin, P. A. Bakhvalov, V. G. Bobkov, A. V. Gorobets, “Parallel algorithm for flow simulation in rotor-stator systems based on edge-bases schemes”, Math. Models Comput. Simul., 13:1 (2021), 172–180
V. G. Bobkov, I. V. Abalakin, T. K. Kozubskaya, “Metodika rascheta aerodinamicheskikh kharakteristik vintov vertoleta na osnove reberno-orientirovannykh skhem v komplekse programm NOISEtte”, Kompyuternye issledovaniya i modelirovanie, 12:5 (2020), 1097–1122
P. A. Bakhvalov, “Method of local element splittings for diffusion terms discretization in edge-bases schemes”, Preprinty IPM im. M. V. Keldysha, 2020, 079, 43 pp.
A. V. Gorobets, P. A. Bakhvalov, A. P. Duben, P. V. Rodionov, “Acceleration of NOISEtte code for scale-resolving supercomputer simulations of turbulent flows”, Lobachevskii J. Math., 41:8, SI (2020), 1463–1474
Tatiana K. Kozubskaya, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 253
A. V. Gorobets, M. I. Neiman-zade, S. K. Okunev, A. A. Kalyakin, S. A. Soukov, “Performance of Elbrus-8C processor in supercomputer CFD simulations”, Math. Models Comput. Simul., 11:6 (2019), 914–923
P. A. Bakhvalov, “On gradient calculation in flux correction method”, Math. Models Comput. Simul., 12:1 (2020), 12–26
I. V. Abalakin, V. A. Vershkov, N. S. Zhdanova, T. K. Kozubskaya, “Numerical simulation of acoustic fields induced by flow past oscillating solid”, Math. Models Comput. Simul., 12:3 (2020), 422–432
A. Gorobets, “Parallel algorithm of the NOISEtte code for CFD and CAA simulations”, Lobachevskii J. Math., 39:4 (2018), 524–532
P. Bakhvalov, T. Kozubskaya, “Reprint of: EBR-WENO scheme for solving gas dynamics problems with discontinuities on unstructured meshes”, Comput. Fluids, 169, SI (2018), 98–110
P. A. Bakhvalov, “Modelirovanie techeniya v sistemakh rotor–stator s osesimmetrichnym statorom rëberno-orientirovannymi skhemami”, Preprinty IPM im. M. V. Keldysha, 2018, 124, 16 pp.
P. A. Bakhvalov, V. A. Vershkov, “Rëberno-orientirovannye skhemy na podvizhnykh gibridnykh setkakh v kode NOISEtte”, Preprinty IPM im. M. V. Keldysha, 2018, 127, 36 pp.
A. V. Gorobets, M. I. Neiman-zade, S. K. Okunev, A. A. Kalyakin, S. A. Sukov, “Proizvoditelnost protsessora Elbrus-8S v superkompyuternykh prilozheniyakh vychislitelnoi gazovoi dinamiki”, Preprinty IPM im. M. V. Keldysha, 2018, 152, 20 pp.
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