Abstract:
For the three-dimensional Euler equations, a locally one-dimensional bicompact scheme having the fourth order of approximation in space and the second order of approximation in time is considered. The scheme is used in the Taylor–Green vortex problem in an inviscid perfect gas to examine the degree to which a conservative limiting (monotonization) method applied to bicompact schemes affects their theoretically high spectral resolution. Two parallel computational algorithms for locally one-dimensional bicompact schemes are proposed. One of them is used for carrying out computations. It is shown that, in the case of monotonization, the chosen bicompact scheme resolves 70–85% of the kinetic energy spectrum of the fluid. The scheme is compared with high-order accurate WENO55 schemes in terms of the behavior of kinetic energy and enstrophy. It is demonstrated that the bicompact scheme has noticeably lower dissipation and more weakly suppresses medium-scale eddies.
Citation:
M. D. Bragin, “Influence of monotonization on the spectral resolution of bicompact schemes in the inviscid Taylor–Green vortex problem”, Zh. Vychisl. Mat. Mat. Fiz., 62:4 (2022), 625–641; Comput. Math. Math. Phys., 62:4 (2022), 608–623
\Bibitem{Bra22}
\by M.~D.~Bragin
\paper Influence of monotonization on the spectral resolution of bicompact schemes in the inviscid Taylor--Green vortex problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 4
\pages 625--641
\mathnet{http://mi.mathnet.ru/zvmmf11386}
\crossref{https://doi.org/10.31857/S0044466922040032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4431089}
\elib{https://elibrary.ru/item.asp?id=48340798}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 4
\pages 608--623
\crossref{https://doi.org/10.1134/S0965542522040030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130810190}
Linking options:
https://www.mathnet.ru/eng/zvmmf11386
https://www.mathnet.ru/eng/zvmmf/v62/i4/p625
This publication is cited in the following 4 articles:
M. D. Bragin, N. V. Zmitrenko, V. V. Zmushko, P. A. Kuchugov, E. V. Levkina, K. V. Anisiforov, N. V. Nevmerzhitskiy, A. N. Razin, E. D. Sen'kovskiy, V. P. Statsenko, N. V. Tishkin, Yu. V. Tret'yachenko, Yu. V. Yanilkin, “Mathematical modeling of turbulent mixing in gas systems with a chevron contact boundary using NUT3D, BIC3D, EGAK, and MIMOSA numerical codes”, Programmirovanie, 2024, no. 1
M. D. Bragin, “Numerical modeling of compressible mixing layers with a bicompact scheme”, Math. Models Comput. Simul., 16:4 (2024), 521–535
Y. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for three-dimensional Euler equations”, Math. Models Comput. Simul., 16:6 (2024), 843–852
M. D. Bragin, N. V. Zmitrenko, V. V. Zmushko, P. A. Kuchugov, E. V. Levkina, K. V. Anisiforov, N. V. Nevmerzhitskiy, A. N. Razin, E. D. Senkovskiy, V. P. Statsenko, V. F. Tishkin, Yu. V. Tret'yachenko, Yu. V. Yanilkin, “Mathematical Modeling of Turbulent Mixing in Gas Systems with a Chevron Contact Boundary using NUT3D, BIC3D, EGAK, and MIMOSA Numerical Codes”, Program Comput Soft, 49:8 (2023), 854
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