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Matematicheskie Zametki, 2021, Volume 110, Issue 5, paper published in the English version journal (Mi mzm13341)  

This article is cited in 1 scientific paper (total in 1 paper)

Papers published in the English version of the journal

Hugoniot–Maslov Chain for Shock Waves in Buckley–Leverett Equations

P. Rodríguez-Bermúdeza, F. V. Sousab, D. C. Lobãoa, G. B. Alvareza, B. Valiño-Alonsoc

a Department of Exact Sciences, Federal Fluminense University, Volta Redonda, Rio de Janeiro, 27255125 Brazil
b Federal Fluminense University, Volta Redonda, Rio de Janeiro, 27255125 Brazil
c Differential Equations Department, Havana University, Havana, 10400 Cuba
Citations (1)
Abstract: In this paper, we apply the asymptotic method developed by V. P. Maslov [1] to obtain the approximated shock-type solutions of the generalized Riemann problem (GRP) to the Buckley–Leverett equation. We calculate the the Hugoniot–Maslov chain (an infinite ODE system) whose fulfillment is a necessary condition that must be satisfied by the coefficients of the asymptotic expansion of the shock-type solution. Numerical simulations based on the truncated Hugoniot–Maslov chain show the efficiency of this method which captures the shock wave unlike some classical finite differences schemes. Finally, we compare the results obtained in this paper with the results obtained via the same asymptotic method, but based in a previous polynomial approximation of the Buckley–Leverett flux as explained in [2]. It was observed that the application of the asymptotic method preceded by a polynomial approximation of the flux function, does not work well for long time simulation values.
Keywords: asymptotic methods, shock waves, the Buckley–Leverett equation, generalized Riemann problem, the Hugoniot–Maslov chain.
Funding agency Grant number
Coordenaҫão de Aperfeiҫoamento de Pessoal de Nível Superior
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
National Council for Scientific and Technological Development (CNPq)
Universidade Federal Fluminense
The authors acknowledge the financial support provided by the Brazilian funding agencies CAPES, FAPERJ, CNPq, and UFF-Federal Fluminense University.
Received: 03.03.2020
Revised: 19.02.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 5, Pages 738–753
DOI: https://doi.org/10.1134/S0001434621110110
Bibliographic databases:
Document Type: Article
Language: English
Citation: P. Rodríguez-Bermúdez, F. V. Sousa, D. C. Lobão, G. B. Alvarez, B. Valiño-Alonso, “Hugoniot–Maslov Chain for Shock Waves in Buckley–Leverett Equations”, Math. Notes, 110:5 (2021), 738–753
Citation in format AMSBIB
\Bibitem{RodSouLob21}
\by P.~Rodr{\'\i}guez-Berm\'udez, F.~V.~Sousa, D.~C.~Lob\~ao, G.~B.~Alvarez, B.~Vali\~no-Alonso
\paper Hugoniot--Maslov Chain for Shock Waves
in Buckley--Leverett Equations
\jour Math. Notes
\yr 2021
\vol 110
\issue 5
\pages 738--753
\mathnet{http://mi.mathnet.ru/mzm13341}
\crossref{https://doi.org/10.1134/S0001434621110110}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000730355100011}
\elib{https://elibrary.ru/item.asp?id=47866124}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85121380847}
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    Математические заметки Mathematical Notes
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