Abstract:
A finite-difference TVD scheme is presented for problems in nonequilibrium wave dynamics of heterogeneous media with different velocities and temperatures but with identical pressures of the phases. A nonlinear form of artificial viscosity depending on the phase relaxation time is proposed. The computed solutions are compared with exact self-similar ones for an equilibrium heterogeneous medium. The performance of the scheme is demonstrated by numerical simulation with varying particle diameters, grid sizes, and particle concentrations. It is shown that the scheme is efficient in terms of Fletcher's criterion as applied to stiff problems.
Key words:
TVD scheme, dynamics of heterogeneous media, stiff problem.
Citation:
D. V. Sadin, “TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type”, Zh. Vychisl. Mat. Mat. Fiz., 56:12 (2016), 2098–2109; Comput. Math. Math. Phys., 56:12 (2016), 2068–2078
\Bibitem{Sad16}
\by D.~V.~Sadin
\paper TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 12
\pages 2098--2109
\mathnet{http://mi.mathnet.ru/zvmmf10499}
\crossref{https://doi.org/10.7868/S0044466916120152}
\elib{https://elibrary.ru/item.asp?id=27640193}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 12
\pages 2068--2078
\crossref{https://doi.org/10.1134/S0965542516120137}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391821900010}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10499
https://www.mathnet.ru/eng/zvmmf/v56/i12/p2098
This publication is cited in the following 22 articles:
E. N. Shirokova, D. V. Sadin, “Volnovye i relaksatsionnye effekty pri istechenii gazovzvesi, chastichno zapolnyayuschei tsilindricheskii kanal”, Kompyuternye issledovaniya i modelirovanie, 15:6 (2023), 1495–1506
D. V. Sadin, “Test problems of gas suspension dynamics using asymptotically exact solutions”, Math. Models Comput. Simul., 15:3 (2023), 564–573
D. V. Sadin, “Efficient implementation of the hybrid large-particle method”, Math. Models Comput. Simul., 14:6 (2022), 946–954
D. A. Gubaidullin, D. A. Tukmakov, “Numerical modeling of the shock waves reflection from a firm surface in mono- and polydisperse gas suspensions”, Lobachevskii J. Math., 42:1 (2021), 104–109
D. V. Sadin, I. O. Golikov, E. N. Shirokova, “Testing of the hybrid large-particle method using two-dimensional Riemann problems”, St. Petersb. Polytech. Univ. J.-Phys. Math., 14:1 (2021), 58–71
D. V. Sadin, “Numerical dynamics scenarios of a variable in width gas suspension layer accelerated by a passing shock wave”, St. Petersb. Polytech. Univ. J.-Phys. Math., 14:2 (2021), 53–64
D. V. Sadin, “Numerical and analytical study of gas suspension expansion in a closed shock tube”, St. Petersb. Polytech. Univ. J.-Phys. Math., 14:4 (2021), 40–49
D. A. Tukmakov, “Chislennoe issledovanie intensivnykh udarnykh voln v zapylennykh sredakh s odnorodnoi i dvukhkomponentnoi nesuschei fazoi”, Kompyuternye issledovaniya i modelirovanie, 12:1 (2020), 141–154
D. V. Sadin, “Analiz dissipativnykh svoistv gibridnogo metoda krupnykh chastits dlya strukturno slozhnykh techenii gaza”, Kompyuternye issledovaniya i modelirovanie, 12:4 (2020), 757–772
D. V. Sadin, B. V. Belyaev, V. A. Davidchuk, “Vliyanie relaksatsionnykh protsessov na fokusirovku udarnoi volny v oblake gazovzvesi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 66, 121–131
D. V. Sadin, “Prilozhenie gibridnogo metoda krupnykh chastits k raschetu vzaimodeistviya udarnoi volny so sloem gazovzvesi”, Kompyuternye issledovaniya i modelirovanie, 12:6 (2020), 1323–1338
D. A. Tukmakov, A. A. Akhunov, “Chislennoe issledovanie rasprostraneniya udarnoi volny maloi intensivnosti iz chistogo gaza v elektricheski zaryazhennuyu zapylennuyu sredu”, Chebyshevskii sb., 21:4 (2020), 257–269
O. P. Stoyanovskaya, F. A. Okladnikov, E. I. Vorobyov, Ya. N. Pavlyuchenkov, V. V. Akimkin, “Simulations of dynamical gas-dust circumstellar disks: going beyond the Epstein regime”, Astron. Rep., 64:2 (2020), 107–125
V D. Sadin , V. A. Davidchuk, “Interaction of a plane shock wave with regions of varying shape and density in a finely divided gas suspension”, J. Eng. Phys. Thermophys., 93:2 (2020), 474–483
D. A. Tukmakov, “Numerical investigation of the influence of properties of the gas component of a suspension of solid particles on the spreading of a compressed gas-suspension volume in a binary medium”, J. Eng. Phys. Thermophys., 93:2 (2020), 291–297
D. A. Tukmakov, A. A. Akhunov, “Chislennoe issledovanie vliyaniya elektricheskogo zaryada dispersnoi fazy na rasprostranenie udarnoi volny iz chistogo gaza v zapylennuyu sredu”, Izv. Sarat. un-ta. Nov. cer. Ser. Fizika, 20:3 (2020), 183–192
D. V. Sadin, V. A. Davidchuk, “Osobennosti rascheta vzaimodeistviya udarnoi volny s gazovym puzyrem v melkodispersnoi gazovzvesi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2019, no. 57, 99–110
D. V. Sadin, “Modifikatsiya metoda krupnykh chastits do skhemy vtorogo poryadka tochnosti po prostranstvu i vremeni dlya udarno-volnovykh techenii gazovzvesi”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:2 (2019), 112–122
D. A. Tukmakov, “Chislennoe modelirovanie kolebanii elektricheski zaryazhennoi geterogennoi sredy, obuslovlennykh mezhkomponentnym vzaimodeistviem”, Izvestiya vuzov. PND, 27:3 (2019), 73–85
D. A. Tukmakov, “Numerical study of velocity slip of phases during the passage of a shock wave of low intensity from a pure gas to a dusty medium”, Proceedings of the Mavlyutov Institute of Mechanics, 14:2 (2019), 125–131
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