{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T20:57:55Z","timestamp":1777755475014,"version":"3.51.4"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001502","name":"Department of Atomic Energy, Government of India","doi-asserted-by":"publisher","award":["12-R &D-TFR-5.01-0520"],"award-info":[{"award-number":["12-R &D-TFR-5.01-0520"]}],"id":[{"id":"10.13039\/501100001502","id-type":"DOI","asserted-by":"publisher"}]},{"name":"DST-SERB, MATRICS","award":["MTR\/2019\/000380"],"award-info":[{"award-number":["MTR\/2019\/000380"]}]},{"name":"VAJRA Grant","award":["VJR-2018-000129"],"award-info":[{"award-number":["VJR-2018-000129"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s10915-023-02387-z","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T19:02:35Z","timestamp":1699297355000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Entropy Stable Discontinuous Galerkin Schemes for Two-Fluid Relativistic Plasma Flow Equations"],"prefix":"10.1007","volume":"97","author":[{"given":"Deepak","family":"Bhoriya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biswarup","family":"Biswas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harish","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Praveen","family":"Chandrashekhar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"issue":"1","key":"2387_CR1","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1115\/1.3625776","volume":"32","author":"M Abramowitz","year":"1965","unstructured":"Abramowitz, M., Stegun, I.A., Miller, D.: Handbook of mathematical functions with formulas, graphs and mathematical tables (National Bureau of Standards applied mathematics series no. 55). J. Appl. Mech. 32(1), 239\u2013239 (1965). https:\/\/doi.org\/10.1115\/1.3625776","journal-title":"J. Appl. Mech."},{"issue":"1","key":"2387_CR2","doi-asserted-by":"publisher","first-page":"100","DOI":"10.3847\/0004-637x\/831\/1\/100","volume":"831","author":"T Amano","year":"2016","unstructured":"Amano, T.: A second-order divergence-constrained multidimensional numerical scheme for relativistic two-fluid electrodynamics. Astrophys. J. 831(1), 100 (2016). https:\/\/doi.org\/10.3847\/0004-637x\/831\/1\/100","journal-title":"Astrophys. J."},{"issue":"1","key":"2387_CR3","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1088\/0004-637X\/770\/1\/18","volume":"770","author":"T Amano","year":"2013","unstructured":"Amano, T., Kirk, J.G.: The role of superluminal electromagnetic waves in pulsar wind termination shocks. Astrophys. J. 770(1), 18 (2013). https:\/\/doi.org\/10.1088\/0004-637X\/770\/1\/18","journal-title":"Astrophys. J."},{"key":"2387_CR4","doi-asserted-by":"publisher","unstructured":"Anile, A.M.: Relativistic Fluids and Magneto-fluids. Cambridge Press, New York (1990). https:\/\/doi.org\/10.1017\/cbo9780511564130","DOI":"10.1017\/cbo9780511564130"},{"issue":"1","key":"2387_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/0067-0049\/188\/1\/1","volume":"188","author":"L Anton","year":"2010","unstructured":"Anton, L., Miralles, J.A., Marti, J.M., Ibez, J.M., Aloy, M.A., Mimica, P.: Relativistic magnetohydrodynamics: renormalized eigenvectors and full wave decomposition Riemann solver. Astrophys. J. Suppl. Ser. 188(1), 1\u201331 (2010). https:\/\/doi.org\/10.1088\/0067-0049\/188\/1\/1","journal-title":"Astrophys. J. Suppl. Ser."},{"issue":"4\u20136","key":"2387_CR6","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S0378-4754(00)00310-4","volume":"55","author":"S Baboolal","year":"2001","unstructured":"Baboolal, S.: Finite-difference modeling of solitons induced by a density hump in a plasma multi-fluid. Math. Comput. Simul. 55(4\u20136), 309\u2013316 (2001). https:\/\/doi.org\/10.1016\/S0378-4754(00)00310-4","journal-title":"Math. Comput. Simul."},{"issue":"1","key":"2387_CR7","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1086\/318941","volume":"132","author":"D Balsara","year":"2001","unstructured":"Balsara, D.: Total variation diminishing scheme for relativistic magnetohydrodynamics. Astrophys. J. Suppl. Ser. 132(1), 83\u2013101 (2001). https:\/\/doi.org\/10.1086\/318941","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"2387_CR8","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.jcp.2016.05.006","volume":"318","author":"DS Balsara","year":"2016","unstructured":"Balsara, D.S., Amano, T., Garain, S., Kim, J.: A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism. J. Comput. Phys. 318, 169\u2013200 (2016). https:\/\/doi.org\/10.1016\/j.jcp.2016.05.006","journal-title":"J. Comput. Phys."},{"key":"2387_CR9","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.jcp.2016.02.001","volume":"312","author":"DS Balsara","year":"2016","unstructured":"Balsara, D.S., Kim, J.: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector. J. Comput. Phys. 312, 357\u2013384 (2016). https:\/\/doi.org\/10.1016\/j.jcp.2016.02.001","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR10","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1093\/mnras\/stt2247","volume":"438","author":"M Barkov","year":"2014","unstructured":"Barkov, M., Komissarov, S.S., Korolev, V., Zankovich, A.: A multidimensional numerical scheme for two-fluid relativistic magnetohydrodynamics. Mon. Not. R. Astron. Soc. 438(1), 704\u2013716 (2014). https:\/\/doi.org\/10.1093\/mnras\/stt2247","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"2387_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-020-1250-8","author":"D Bhoriya","year":"2020","unstructured":"Bhoriya, D., Kumar, H.: Entropy-stable schemes for relativistic hydrodynamics equations. Z. Angew. Math. Phys. (2020). https:\/\/doi.org\/10.1007\/s00033-020-1250-8","journal-title":"Z. Angew. Math. Phys."},{"key":"2387_CR12","doi-asserted-by":"crossref","unstructured":"Bhoriya, D., Kumar, H., Chandrashekar, P.: High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations (2022). ArXiv:2210.08568 [physics]","DOI":"10.1016\/j.jcp.2023.112207"},{"issue":"A3","key":"2387_CR13","doi-asserted-by":"publisher","first-page":"3715","DOI":"10.1029\/1999ja900449","volume":"106","author":"J Birn","year":"2001","unstructured":"Birn, J., Drake, J.F., Shay, M.A., Rogers, B.N., Denton, R.E., Hesse, M., Kuznetsova, M., Ma, Z.W., Bhattacharjee, A., Otto, A., Pritchett, P.L.: Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. Sp. Phys. 106(A3), 3715\u20133719 (2001). https:\/\/doi.org\/10.1029\/1999ja900449","journal-title":"J. Geophys. Res. Sp. Phys."},{"key":"2387_CR14","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.camwa.2022.02.019","volume":"112","author":"B Biswas","year":"2022","unstructured":"Biswas, B., Kumar, H., Bhoriya, D.: Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations. Comput. Math. Appl. 112, 55\u201375 (2022). https:\/\/doi.org\/10.1016\/j.camwa.2022.02.019","journal-title":"Comput. Math. Appl."},{"key":"2387_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110148","volume":"431","author":"B Biswas","year":"2021","unstructured":"Biswas, B., Kumar, H., Yadav, A.: Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations. J. Comput. Phys. 431, 110148 (2021). https:\/\/doi.org\/10.1016\/j.jcp.2021.110148","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR16","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1146\/annurev-astro-081817-051948","volume":"57","author":"R Blandford","year":"2019","unstructured":"Blandford, R., Meier, D., Readhead, A.: Relativistic jets from active galactic nuclei. Ann. Rev. Astron. Astrophys. 57(1), 467\u2013509 (2019). https:\/\/doi.org\/10.1146\/annurev-astro-081817-051948","journal-title":"Ann. Rev. Astron. Astrophys."},{"key":"2387_CR17","unstructured":"Bond, D.M., Wheatley, V., Samtaney, R.: Plasma flow simulation using the two-fluid model. In: Proceedings of the 20th Australasian Fluid Mechanics Conference, AFMC 2016 (2016)"},{"issue":"5","key":"2387_CR18","doi-asserted-by":"publisher","first-page":"B835","DOI":"10.1137\/130932193","volume":"36","author":"MH Carpenter","year":"2014","unstructured":"Carpenter, M.H., Fisher, T.C., Nielsen, E.J., Frankel, S.H.: Entropy stable spectral collocation schemes for the Navier-Stokes equations: discontinuous interfaces. SIAM J. Sci. Comput. 36(5), B835\u2013B867 (2014). https:\/\/doi.org\/10.1137\/130932193","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"2387_CR19","doi-asserted-by":"publisher","first-page":"1252","DOI":"10.4208\/cicp.170712.010313a","volume":"14","author":"P Chandrashekar","year":"2013","unstructured":"Chandrashekar, P.: Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations. Commun. Comput. Phys. 14(5), 1252\u20131286 (2013). https:\/\/doi.org\/10.4208\/cicp.170712.010313a","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"2387_CR20","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1137\/15M1013626","volume":"54","author":"P Chandrashekar","year":"2016","unstructured":"Chandrashekar, P., Klingenberg, C.: Entropy stable finite volume scheme for ideal compressible MHD on 2-D cartesian meshes. SIAM J. Numer. Anal. 54(2), 1313\u20131340 (2016). https:\/\/doi.org\/10.1137\/15M1013626","journal-title":"SIAM J. Numer. Anal."},{"key":"2387_CR21","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/j.jcp.2017.05.025","volume":"345","author":"T Chen","year":"2017","unstructured":"Chen, T., Shu, C.W.: Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. J. Comput. Phys. 345, 427\u2013461 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.05.025","journal-title":"J. Comput. Phys."},{"issue":"7","key":"2387_CR22","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1002\/cpa.21537","volume":"68","author":"E Chiodaroli","year":"2015","unstructured":"Chiodaroli, E., De Lellis, C., Kreml, O.: Global ill-posedness of the isentropic system of gas dynamics. Commun. Pure Appl. Math. 68(7), 1157\u20131190 (2015). https:\/\/doi.org\/10.1002\/cpa.21537","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"2387_CR23","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1051\/0004-6361:20077093","volume":"473","author":"L Del Zanna","year":"2007","unstructured":"Del Zanna, L., Zanotti, O., Bucciantini, N., Londrillo, P.: ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics. Astron. Astrophys. 473(1), 11\u201330 (2007). https:\/\/doi.org\/10.1051\/0004-6361:20077093","journal-title":"Astron. Astrophys."},{"key":"2387_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109731","volume":"421","author":"J Duan","year":"2020","unstructured":"Duan, J., Tang, H.: High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics. J. Comput. Phys. 421, 109731 (2020). https:\/\/doi.org\/10.1016\/j.jcp.2020.109731","journal-title":"J. Comput. Phys."},{"key":"2387_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/J.JCP.2020.109949","volume":"426","author":"J Duan","year":"2021","unstructured":"Duan, J., Tang, H.: Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics. J. Comput. Phys. 426, 109949 (2021). https:\/\/doi.org\/10.1016\/J.JCP.2020.109949","journal-title":"J. Comput. Phys."},{"key":"2387_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110136","volume":"431","author":"J Duan","year":"2021","unstructured":"Duan, J., Tang, H.: High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics. J. Comput. Phys. 431, 110136 (2021). https:\/\/doi.org\/10.1016\/j.jcp.2021.110136","journal-title":"J. Comput. Phys."},{"key":"2387_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111038","volume":"456","author":"J Duan","year":"2022","unstructured":"Duan, J., Tang, H.: High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics. J. Comput. Phys. 456, 111038 (2022). https:\/\/doi.org\/10.1016\/j.jcp.2022.111038","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2387_CR28","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1093\/MNRAS\/278.2.586","volume":"278","author":"SA Falle","year":"1996","unstructured":"Falle, S.A., Komissarov, S.S.: An upwind numerical scheme for relativistic hydrodynamics with a general equation of state. Mon. Not. R. Astron. Soc. 278(2), 586\u2013602 (1996). https:\/\/doi.org\/10.1093\/MNRAS\/278.2.586","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"2","key":"2387_CR29","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1137\/110836961","volume":"50","author":"US Fjordholm","year":"2012","unstructured":"Fjordholm, U.S., Mishra, S., Tadmor, E.: Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws. SIAM J. Numer. Anal. 50(2), 544\u2013573 (2012). https:\/\/doi.org\/10.1137\/110836961","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"2387_CR30","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10208-012-9117-9","volume":"13","author":"US Fjordholm","year":"2013","unstructured":"Fjordholm, U.S., Mishra, S., Tadmor, E.: ENO reconstruction and ENO interpolation are stable. Found. Comput. Math. 13(2), 139\u2013159 (2013). https:\/\/doi.org\/10.1007\/s10208-012-9117-9","journal-title":"Found. Comput. Math."},{"issue":"1","key":"2387_CR31","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s10915-019-00933-2","volume":"80","author":"L Friedrich","year":"2019","unstructured":"Friedrich, L., Schn\u00fccke, G., Winters, A.R., Fern\u00e1ndez, D.C.R., Gassner, G.J., Carpenter, M.H.: Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws. J. Sci. Comput. 80(1), 175\u2013222 (2019). https:\/\/doi.org\/10.1007\/s10915-019-00933-2","journal-title":"J. Sci. Comput."},{"key":"2387_CR32","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1086\/174810","volume":"435","author":"YA Gallant","year":"1994","unstructured":"Gallant, Y.A., Arons, J.: Structure of relativistic shocks in pulsar winds: a model of the wisps in the Crab Nebula. Astrophys. J. 435, 230 (1994). https:\/\/doi.org\/10.1086\/174810","journal-title":"Astrophys. J."},{"issue":"1","key":"2387_CR33","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s00574-016-0142-1","volume":"47","author":"JP Gallego-Valencia","year":"2016","unstructured":"Gallego-Valencia, J.P., Klingenberg, C., Chandrashekar, P.: On limiting for higher order discontinuous Galerkin method for 2D Euler equations. Bull. Braz. Math. Soc. 47(1), 335\u2013345 (2016). https:\/\/doi.org\/10.1007\/s00574-016-0142-1","journal-title":"Bull. Braz. Math. Soc."},{"issue":"1","key":"2387_CR34","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1086\/374594","volume":"589","author":"CF Gammie","year":"2003","unstructured":"Gammie, C.F., McKinney, J.C., Toth, G.: HARM: a numerical scheme for general relativistic magnetohydrodynamics. Astrophys. J. 589(1), 444\u2013457 (2003). https:\/\/doi.org\/10.1086\/374594","journal-title":"Astrophys. J."},{"key":"2387_CR35","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.amc.2015.07.014","volume":"272","author":"GJ Gassner","year":"2016","unstructured":"Gassner, G.J., Winters, A.R., Kopriva, D.A.: A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. Appl. Math. Comput. 272, 291\u2013308 (2016). https:\/\/doi.org\/10.1016\/j.amc.2015.07.014","journal-title":"Appl. Math. Comput."},{"key":"2387_CR36","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.jcp.2016.09.013","volume":"327","author":"GJ Gassner","year":"2016","unstructured":"Gassner, G.J., Winters, A.R., Kopriva, D.A.: Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys. 327, 39\u201366 (2016). https:\/\/doi.org\/10.1016\/j.jcp.2016.09.013","journal-title":"J. Comput. Phys."},{"key":"2387_CR37","volume-title":"Hyperbolic Systems of Conservation Laws","author":"E Godlewski","year":"1991","unstructured":"Godlewski, E., Pierre-Arnaud, R.: Hyperbolic Systems of Conservation Laws. Ellipses-Edition Marketing, Paris (1991)"},{"issue":"1","key":"2387_CR38","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1137\/S003614450036757X","volume":"43","author":"S Gottlieb","year":"2001","unstructured":"Gottlieb, S., Shu, C.W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89\u2013112 (2001). https:\/\/doi.org\/10.1137\/S003614450036757X","journal-title":"SIAM Rev."},{"issue":"1","key":"2387_CR39","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1016\/j.jcp.2006.03.036","volume":"219","author":"A Hakim","year":"2006","unstructured":"Hakim, A., Loverich, J., Shumlak, U.: A high resolution wave propagation scheme for ideal Two-Fluid plasma equations. J. Comput. Phys. 219(1), 418\u2013442 (2006). https:\/\/doi.org\/10.1016\/j.jcp.2006.03.036","journal-title":"J. Comput. Phys."},{"key":"2387_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-72067-8","volume-title":"Nodal Discontinuous Galerkin Methods: Algorithmus, Analysis, and Applications, Texts in Applied Mathematics","author":"JS Hesthaven","year":"2000","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithmus, Analysis, and Applications, Texts in Applied Mathematics, vol. 54. Springer New York, New York (2000). https:\/\/doi.org\/10.1007\/978-0-387-72067-8"},{"issue":"15","key":"2387_CR41","doi-asserted-by":"publisher","first-page":"5410","DOI":"10.1016\/j.jcp.2009.04.021","volume":"228","author":"F Ismail","year":"2009","unstructured":"Ismail, F., Roe, P.L.: Affordable, entropy-consistent Euler flux functions II: entropy production at shocks. J. Comput. Phys. 228(15), 5410\u20135436 (2009). https:\/\/doi.org\/10.1016\/j.jcp.2009.04.021","journal-title":"J. Comput. Phys."},{"key":"2387_CR42","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1016\/j.jcp.2014.04.023","volume":"270","author":"J Kim","year":"2014","unstructured":"Kim, J., Balsara, D.S.: A stable HLLC Riemann solver for relativistic magnetohydrodynamics. J. Comput. Phys. 270, 634\u2013639 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.04.023","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2387_CR43","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1046\/j.1365-8711.1999.02244.x","volume":"303","author":"SS Komissarov","year":"1999","unstructured":"Komissarov, S.S.: A Godunov-type scheme for relativistic magnetohydrodynamics. Mon. Not. R. Astron. Soc. 303(2), 343\u2013366 (1999). https:\/\/doi.org\/10.1046\/j.1365-8711.1999.02244.x","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"3","key":"2387_CR44","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1111\/j.1365-2966.2007.12448.x","volume":"382","author":"SS Komissarov","year":"2007","unstructured":"Komissarov, S.S.: Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics. Mon. Not. R. Astron. Soc. 382(3), 995\u20131004 (2007). https:\/\/doi.org\/10.1111\/j.1365-2966.2007.12448.x","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"2","key":"2387_CR45","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s10915-011-9554-7","volume":"52","author":"H Kumar","year":"2012","unstructured":"Kumar, H., Mishra, S.: Entropy stable numerical schemes for two-fluid plasma equations. J. Sci. Comput. 52(2), 401\u2013425 (2012). https:\/\/doi.org\/10.1007\/s10915-011-9554-7","journal-title":"J. Sci. Comput."},{"key":"2387_CR46","doi-asserted-by":"publisher","unstructured":"Landau, L.D., Lifshitz, E.M.: Chapter XV - Relativistic fluid dynamics. In: L.D. Landau, E.M. Lifshitz (eds.) Fluid Mechanics, 2nd edn, pp. 505\u2013514. Pergamon (1987). https:\/\/doi.org\/10.1016\/b978-0-08-033933-7.50023-4","DOI":"10.1016\/b978-0-08-033933-7.50023-4"},{"key":"2387_CR47","doi-asserted-by":"publisher","DOI":"10.1017\/cbo9780511791253","volume-title":"Finite Volume Methods for Hyperbolic Problems","author":"RJ LeVeque","year":"2002","unstructured":"LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002). https:\/\/doi.org\/10.1017\/cbo9780511791253"},{"key":"2387_CR48","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.jcp.2017.10.043","volume":"354","author":"Y Liu","year":"2018","unstructured":"Liu, Y., Shu, C.W., Zhang, M.: Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes. J. Comput. Phys. 354, 163\u2013178 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2017.10.043","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/JCPH.1996.0001","volume":"123","author":"JM Mart\u00ed","year":"1996","unstructured":"Mart\u00ed, J.M., M\u00fcller, E.: Extension of the piecewise parabolic method to one-dimensional relativistic hydrodynamics. J. Comput. Phys. 123(1), 1\u201314 (1996). https:\/\/doi.org\/10.1006\/JCPH.1996.0001","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR50","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/LRCA-2015-3","volume":"1","author":"JM Mart\u00ed","year":"2015","unstructured":"Mart\u00ed, J.M., M\u00fcller, E.: Grid-based methods in relativistic hydrodynamics and magnetohydrodynamics. Living Rev. Comput. Astrophys. 1(1), 1\u2013182 (2015). https:\/\/doi.org\/10.1007\/LRCA-2015-3","journal-title":"Living Rev. Comput. Astrophys."},{"issue":"1","key":"2387_CR51","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1093\/mnras\/stab3373","volume":"510","author":"G Mattia","year":"2021","unstructured":"Mattia, G., Mignone, A.: A comparison of approximate non-linear Riemann solvers for relativistic MHD. Mon. Not. R. Astron. Soc. 510(1), 481\u2013499 (2021). https:\/\/doi.org\/10.1093\/mnras\/stab3373","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"3","key":"2387_CR52","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1111\/j.1365-2966.2006.10162.x","volume":"368","author":"A Mignone","year":"2006","unstructured":"Mignone, A., Bodo, G.: An HLLC Riemann solver for relativistic flows\u2014II Magnetohydrodynamics. Mon. Not. R. Astron. Soc. 368(3), 1040\u20131054 (2006). https:\/\/doi.org\/10.1111\/j.1365-2966.2006.10162.x","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"1","key":"2387_CR53","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1086\/430905\/FULLTEXT\/","volume":"160","author":"A Mignone","year":"2005","unstructured":"Mignone, A., Plewa, T., Bodo, G.: The piecewise parabolic method for multidimensional relativistic fluid dynamics. Astrophys. J. Suppl. Ser. 160(1), 199\u2013219 (2005). https:\/\/doi.org\/10.1086\/430905\/FULLTEXT\/","journal-title":"Astrophys. J. Suppl. Ser."},{"issue":"1\u20132","key":"2387_CR54","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/BF00658666","volume":"231","author":"R Mochkovitch","year":"1995","unstructured":"Mochkovitch, R., Maitia, V., Marques, R.: Internal shocks in a relativistic wind as a source for gamma-ray bursts? Astrophys. Sp. Sci. 231(1\u20132), 441\u2013444 (1995). https:\/\/doi.org\/10.1007\/BF00658666","journal-title":"Astrophys. Sp. Sci."},{"issue":"2","key":"2387_CR55","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1006\/jcph.2000.6507","volume":"161","author":"CD Munz","year":"2000","unstructured":"Munz, C.D., Omnes, P., Schneider, R., Sonnendr\u00fccker, E., Vo\u00df, U.: Divergence correction techniques for Maxwell solvers based on a hyperbolic model. J. Comput. Phys. 161(2), 484\u2013511 (2000). https:\/\/doi.org\/10.1006\/jcph.2000.6507","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR56","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1017\/S002211207900210X","volume":"90","author":"SA Orszag","year":"1979","unstructured":"Orszag, S.A., Tang, C.M.: Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90(1), 129\u2013143 (1979). https:\/\/doi.org\/10.1017\/S002211207900210X","journal-title":"J. Fluid Mech."},{"key":"2387_CR57","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.jcp.2016.02.079","volume":"315","author":"T Qin","year":"2016","unstructured":"Qin, T., Shu, C.W., Yang, Y.: Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics. J. Comput. Phys. 315, 323\u2013347 (2016). https:\/\/doi.org\/10.1016\/j.jcp.2016.02.079","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2387_CR58","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1086\/505937","volume":"166","author":"D Ryu","year":"2006","unstructured":"Ryu, D., Chattopadhyay, I., Choi, E.: Equation of state in numerical relativistic hydrodynamics. Astrophys. J. Suppl. Ser. 166(1), 410\u2013420 (2006). https:\/\/doi.org\/10.1086\/505937","journal-title":"Astrophys. J. Suppl. Ser."},{"issue":"1","key":"2387_CR59","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1006\/jcph.1993.1056","volume":"105","author":"V Schneider","year":"1993","unstructured":"Schneider, V., Katscher, U., Rischke, D.H., Waldhauser, B., Maruhn, J.A., Munz, C.D.: New algorithms for ultra-relativistic numerical hydrodynamics. J. Comput. Phys. 105(1), 92\u2013107 (1993). https:\/\/doi.org\/10.1006\/jcph.1993.1056","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2387_CR60","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1007\/s10915-017-0579-4","volume":"75","author":"C Sen","year":"2018","unstructured":"Sen, C., Kumar, H.: Entropy stable schemes for ten-moment Gaussian closure equations. J. Sci. Comput. 75(2), 1128\u20131155 (2018). https:\/\/doi.org\/10.1007\/s10915-017-0579-4","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2387_CR61","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1016\/S0021-9991(03)00151-7","volume":"187","author":"U Shumlak","year":"2003","unstructured":"Shumlak, U., Loverich, J.: Approximate Riemann solver for the two-fluid plasma model. J. Comput. Phys. 187(2), 620\u2013638 (2003). https:\/\/doi.org\/10.1016\/S0021-9991(03)00151-7","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2387_CR62","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1137\/S0036142901389025","volume":"40","author":"RJ Spiteri","year":"2002","unstructured":"Spiteri, R.J., Ruuth, S.J.: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40(2), 469\u2013491 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"179","key":"2387_CR63","doi-asserted-by":"publisher","first-page":"91","DOI":"10.2307\/2008251","volume":"49","author":"E Tadmor","year":"1987","unstructured":"Tadmor, E.: The numerical viscosity of entropy stable schemes for systems of conservation laws. I. Math. Comput. 49(179), 91 (1987). https:\/\/doi.org\/10.2307\/2008251","journal-title":"Math. Comput."},{"key":"2387_CR64","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1017\/S0962492902000156","volume":"12","author":"E Tadmor","year":"2003","unstructured":"Tadmor, E.: Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems. Acta Numer. 12, 451\u2013512 (2003). https:\/\/doi.org\/10.1017\/S0962492902000156","journal-title":"Acta Numer."},{"issue":"2","key":"2387_CR65","doi-asserted-by":"publisher","first-page":"L57","DOI":"10.1086\/310196","volume":"467","author":"MHPM van Putten","year":"1996","unstructured":"van Putten, M.H.P.M.: Knots in simulations of magnetized relativistic jets. Astrophys. J. 467(2), L57\u2013L60 (1996). https:\/\/doi.org\/10.1086\/310196","journal-title":"Astrophys. J."},{"issue":"6701","key":"2387_CR66","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1038\/26675","volume":"395","author":"JF Wardle","year":"1998","unstructured":"Wardle, J.F., Homan, D.C., Ojha, R., Roberts, D.H.: Electron-positron jets associated with the quasar 3C279. Nature 395(6701), 457\u2013461 (1998). https:\/\/doi.org\/10.1038\/26675","journal-title":"Nature"},{"key":"2387_CR67","doi-asserted-by":"publisher","unstructured":"Wilson, J.R., Mathews, G.J.: Special relativistic hydrodynamics. In: Relativistic Numerical Hydrodynamics, pp. 23\u201374. Cambridge University Press (2010). https:\/\/doi.org\/10.1017\/cbo9780511615917.003","DOI":"10.1017\/cbo9780511615917.003"},{"issue":"4","key":"2387_CR68","doi-asserted-by":"publisher","first-page":"A2230","DOI":"10.1137\/19M1275590","volume":"42","author":"K Wu","year":"2020","unstructured":"Wu, K., Shu, C.W.: Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. SIAM J. Sci. Comput. 42(4), A2230\u2013A2261 (2020). https:\/\/doi.org\/10.1137\/19M1275590","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"2387_CR69","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s00211-021-01209-4","volume":"148","author":"K Wu","year":"2021","unstructured":"Wu, K., Shu, C.W.: Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. Numer. Math. 148(3), 699\u2013741 (2021). https:\/\/doi.org\/10.1007\/s00211-021-01209-4","journal-title":"Numer. Math."},{"issue":"1","key":"2387_CR70","doi-asserted-by":"publisher","first-page":"3","DOI":"10.3847\/1538-4365\/228\/1\/3","volume":"228","author":"K Wu","year":"2016","unstructured":"Wu, K., Tang, H.: Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state. Astrophys. J. Suppl. Ser. 228(1), 3 (2016). https:\/\/doi.org\/10.3847\/1538-4365\/228\/1\/3","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"2387_CR71","unstructured":"York, J.W. Jr: In: L.L. Smarr (eds.) Sources of Gravitational Radiation, p. 83. Cambridge University Press, New York (1979)"},{"issue":"1","key":"2387_CR72","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1088\/0004-637X\/705\/1\/907","volume":"705","author":"S Zenitani","year":"2009","unstructured":"Zenitani, S., Hesse, M., Klimas, A.: Relativistic two-fluid simulations of guide field magnetic reconnection. Astrophys. J. 705(1), 907\u2013913 (2009). https:\/\/doi.org\/10.1088\/0004-637X\/705\/1\/907","journal-title":"Astrophys. J."},{"issue":"2","key":"2387_CR73","doi-asserted-by":"publisher","first-page":"1385","DOI":"10.1088\/0004-637X\/696\/2\/1385","volume":"696","author":"S Zenitani","year":"2009","unstructured":"Zenitani, S., Hesse, M., Klimas, A.: Two-fluid magnetohydrodynamic simulations of relativistic magnetic reconnection. Astrophys. J. 696(2), 1385\u20131401 (2009). https:\/\/doi.org\/10.1088\/0004-637X\/696\/2\/1385","journal-title":"Astrophys. J."},{"issue":"1","key":"2387_CR74","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1086\/500792\/FULLTEXT\/","volume":"164","author":"W Zhang","year":"2006","unstructured":"Zhang, W., MacFadyen, A.I.: RAM: a relativistic adaptive mesh refinement hydrodynamics code. Astrophys. J. Suppl. Ser. 164(1), 255\u2013279 (2006). https:\/\/doi.org\/10.1086\/500792\/FULLTEXT\/","journal-title":"Astrophys. J. Suppl. Ser."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02387-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02387-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02387-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T20:11:16Z","timestamp":1700597476000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02387-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":74,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["2387"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02387-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,6]]},"assertion":[{"value":"25 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 October 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"72"}}