Abstract:
In this work, a new limiting method for bicompact schemes is proposed that preserves them conservative. The method is based upon a finite-element treatment of the bicompact approximation. An analogy between Galerkin schemes and bicompact schemes is established. The proposed method is tested on one-dimensional gasdynamics problems that include the Sedov problem, the Riemann “peak” problem, and the Shu–Osher problem. It is shown on these examples that bicompact schemes with conservative limiting are significantly more accurate than hybrid bicompact schemes.
\Bibitem{BraRog19}
\by M.~D.~Bragin, B.~V.~Rogov
\paper A conservative limiting method for bicompact schemes
\jour Keldysh Institute preprints
\yr 2019
\papernumber 008
\totalpages 26
\mathnet{http://mi.mathnet.ru/ipmp2646}
\crossref{https://doi.org/10.20948/prepr-2019-8}
\elib{https://elibrary.ru/item.asp?id=36832823}
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This publication is cited in the following 8 articles:
E. N. Aristova, N. I. Karavaeva, A. A. Gurchenkov, “Osobennosti realizatsii modifitsirovannoi skhemy s ermitovoi interpolyatsiei dlya chislennogo resheniya uravneniya perenosa s peremennym koeffitsientom pogloscheniya”, Preprinty IPM im. M. V. Keldysha, 2024, 018, 19 pp.
E. N. Aristova, N. I. Karavaeva, I. R. Ivashkin, “Monotonizatsiya modifitsirovannoi skhemy s ermitovoi interpolyatsiei dlya chislennogo resheniya neodnorodnogo uravneniya perenosa s pogloscheniem”, Preprinty IPM im. M. V. Keldysha, 2024, 065, 40 pp.
E. N. Aristova, N. I. Karavaeva, “The bicompact schemes for numerical solving of Reed problem using HOLO algorithms”, Math. Models Comput. Simul., 14:2 (2022), 187–202
M. D. Bragin, B. V. Rogov, “High-order bicompact schemes for numerical modelling of multispecies multi-reaction gas flows”, Math. Models Comput. Simul., 13:1 (2021), 106–115
E. N. Aristova, N. I. Karavaeva, “Konservativnaya monotonizatsiya varianta CIP skhemy dlya resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2020, 121, 16 pp.
M. D. Bragin, B. V. Rogov, “On the accuracy of bicompact schemes as applied to computation of unsteady shock waves”, Comput. Math. Math. Phys., 60:5 (2020), 864–878
M. D. Bragin, B. V. Rogov, “Bikompaktnye skhemy dlya mnogomernykh uravnenii giperbolicheskogo tipa na dekartovykh setkakh s adaptatsiei k resheniyu”, Preprinty IPM im. M. V. Keldysha, 2019, 011, 27 pp.
Mikhail Dmitrievich Bragin, Boris Vadimovich Rogov, “Bicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR”, KIAM Prepr., 2019, no. 11-e, 1
Citation in format AMSBIB
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