{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:22:02Z","timestamp":1768342922672,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,11,10]],"date-time":"2013-11-10T00:00:00Z","timestamp":1384041600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10915-013-9800-2","type":"journal-article","created":{"date-parts":[[2013,11,9]],"date-time":"2013-11-09T09:58:42Z","timestamp":1383991122000},"page":"363-389","source":"Crossref","is-referenced-by-count":28,"title":["A Class of Incomplete Riemann Solvers Based on Uniform Rational Approximations to the Absolute Value Function"],"prefix":"10.1007","volume":"60","author":[{"given":"Manuel J.","family":"Castro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Gallardo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Marquina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,11,10]]},"reference":[{"key":"9800_CR1","unstructured":"Alouges, F.: Matrice signe et systemes hyperboliques. CMLA Tech. report, ENS Cachan (1998)"},{"key":"9800_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02401828","volume":"37","author":"S Bernstein","year":"1913","unstructured":"Bernstein, S.: Sur la meilleure approximation de $$|x|$$ | x | par del polyn\u00f4mes de degr\u00e9s don\u00e9s. Acta Math. 37, 1\u201357 (1913)","journal-title":"Acta Math."},{"key":"9800_CR3","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/0021-9991(88)90120-9","volume":"75","author":"M Brio","year":"1988","unstructured":"Brio, M., Wu, C.C.: An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 75, 400\u2013422 (1988)","journal-title":"J. Comput. Phys."},{"key":"9800_CR4","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1006\/jath.1998.3206","volume":"95","author":"L Brutman","year":"1998","unstructured":"Brutman, L.: On rational interpolation to $$|x|$$ | x | at the adjusted Chebyshev nodes. J. Approx. Theory 95, 146\u2013152 (1998)","journal-title":"J. Approx. Theory"},{"key":"9800_CR5","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1017\/S0004972700030756","volume":"56","author":"L Brutman","year":"1997","unstructured":"Brutman, L., Passow, E.: Rational interpolation to $$|x|$$ | x | at the Chebyshev nodes. Bull. Aust. Math. Soc. 56, 81\u201386 (1997)","journal-title":"Bull. Aust. Math. Soc."},{"key":"9800_CR6","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF02241866","volume":"44","author":"V Candela","year":"1990","unstructured":"Candela, V., Marquina, A.: Recurrence relations for rational cubic methods I: the Halley method. Computing 44, 169\u2013184 (1990)","journal-title":"Computing"},{"key":"9800_CR7","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1006\/jcph.1997.5773","volume":"136","author":"P Cargo","year":"1997","unstructured":"Cargo, P., Gallice, G.: Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws. J. Comput. Phys. 136, 446\u2013466 (1997)","journal-title":"J. Comput. Phys."},{"key":"9800_CR8","doi-asserted-by":"crossref","first-page":"A2173","DOI":"10.1137\/100795280","volume":"34","author":"MJ Castro D\u00edaz","year":"2012","unstructured":"Castro D\u00edaz, M.J., Fern\u00e1ndez-Nieto, E.D.: A class of computationally fast first order finite volume solvers: PVM methods. SIAM J. Sci. Comput. 34, A2173\u20132196 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"9800_CR9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10915-008-9250-4","volume":"39","author":"MJ Castro D\u00edaz","year":"2009","unstructured":"Castro D\u00edaz, M.J., Fern\u00e1ndez-Nieto, E.D., Ferreiro, A.M., Garc\u00eda, J.A., Par\u00e9s, C.: High order extensions of Roe schemes for two dimensional nonconservative hyperbolic systems. J. Sci. Comput. 39, 67\u2013114 (2009)","journal-title":"J. Sci. Comput."},{"key":"9800_CR10","first-page":"1103","volume":"75","author":"MJ Castro","year":"2006","unstructured":"Castro, M.J., Gallardo, J.M., Par\u00e9s, C.: High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Appl. Shallow Water Syst. Math. Comp. 75, 1103\u20131134 (2006)","journal-title":"Appl. Shallow Water Syst. Math. Comp."},{"key":"9800_CR11","unstructured":"Castro-D\u00edaz, M.J., Fern\u00e1ndez-Nieto, E.D., Narbona-Reina, G., de la Asunci\u00f3n, M.: A two-waves WAF method for nonconservative hyperbolic systems: applications to shallow stratified flows. J. Comput. Phys. (submitted)"},{"key":"9800_CR12","doi-asserted-by":"crossref","unstructured":"Cordier, F., Degond, P., Kumbaro, A.: Phase appearance or disappearance in two-phase flows. J. Sci. Comput. (2013). doi: 10.1007\/s10915-013-9725-9","DOI":"10.1007\/s10915-013-9725-9"},{"key":"9800_CR13","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/S0764-4442(99)80194-3","volume":"328","author":"P Degond","year":"1999","unstructured":"Degond, P., Peyrard, P.F., Russo, G., Villedieu, Ph: Polynomial upwind schemes for hyperbolic systems. C. R. Acad. Sci. Paris S\u00e9r. I 328, 479\u2013483 (1999)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I"},{"key":"9800_CR14","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1006\/jcph.1996.0078","volume":"125","author":"R Donat","year":"1996","unstructured":"Donat, R., Marquina, A.: Capturing shock reflections: an improved flux formula. J. Comput. Phys. 125, 42\u201358 (1996)","journal-title":"J. Comput. Phys."},{"key":"9800_CR15","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0021-9991(91)90211-3","volume":"92","author":"B Einfeldt","year":"1991","unstructured":"Einfeldt, B., Munz, C.D., Roe, P.L., Sj\u00f6green, B.: On Godunov-type methods near low densities. J. Comput. Phys. 92, 273\u2013295 (1991)","journal-title":"J. Comput. Phys."},{"key":"9800_CR16","unstructured":"Guennebaud, G., Jacob B., et al.: Eigen v3. http:\/\/eigen.tuxfamily.org (2010)"},{"key":"9800_CR17","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/1025002","volume":"25","author":"A Harten","year":"1983","unstructured":"Harten, A., Lax, P.D., van Leer, B.: On upstream differencing and Godunov type schemes for hyperbolic conservation laws. SIAM Rev. 25, 35\u201361 (1983)","journal-title":"SIAM Rev."},{"key":"9800_CR18","first-page":"483","volume":"74","author":"G dal Maso","year":"1995","unstructured":"dal Maso, G., LeFloch, P.G., Murat, F.: Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74, 483\u2013548 (1995)","journal-title":"J. Math. Pures Appl."},{"key":"9800_CR19","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1016\/j.nucengdes.2007.11.014","volume":"238","author":"M Ndjinga","year":"2008","unstructured":"Ndjinga, M., Kumbaro, A., de Vuyst, F., Laurent-Gengoux, P.: Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver. Nucl. Eng. Des. 238, 2075\u20132083 (2008)","journal-title":"Nucl. Eng. Des."},{"key":"9800_CR20","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1307\/mmj\/1028999029","volume":"11","author":"DJ Newman","year":"1964","unstructured":"Newman, D.J.: Rational approximation to $$|x|$$ | x | . Mich. Math. J. 11, 11\u201314 (1964)","journal-title":"Mich. Math. J."},{"key":"9800_CR21","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1137\/050628052","volume":"44","author":"C Par\u00e9s","year":"2006","unstructured":"Par\u00e9s, C.: Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal. 44, 300\u2013321 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9800_CR22","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1051\/m2an:2004041","volume":"38","author":"C Par\u00e9s","year":"2004","unstructured":"Par\u00e9s, C., Castro, M.J.: On the well-balance property of Roe\u2019s method for nonconservative hyperbolic systems. Applications to shallow-water systems. M2AN 38, 821\u2013852 (2004)","journal-title":"M2AN"},{"key":"9800_CR23","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1002\/fld.1650180603","volume":"18","author":"JJ Quirk","year":"1994","unstructured":"Quirk, J.J.: A contribution to the great Riemann solver debate. Int. J. Numer. Meth. Fluids 18, 555\u2013574 (1994)","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"9800_CR24","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0021-9991(81)90128-5","volume":"43","author":"PL Roe","year":"1981","unstructured":"Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357\u2013372 (1981)","journal-title":"J. Comput. Phys."},{"key":"9800_CR25","doi-asserted-by":"crossref","first-page":"4232","DOI":"10.1016\/j.jcp.2009.03.001","volume":"228","author":"S Serna","year":"2009","unstructured":"Serna, S.: A characteristic-based nonconvex entropy-fix upwind scheme for the ideal magnetohydrodynamics equations. J. Comput. Phys. 228, 4232\u20134247 (2009)","journal-title":"J. Comput. Phys."},{"key":"9800_CR26","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1093\/imanum\/20.1.47","volume":"20","author":"EF Toro","year":"2000","unstructured":"Toro, E.F., Billett, S.J.: Centred TVD schemes for hyperbolic conservation laws. IMA J. Numer. Anal. 20, 47\u201379 (2000)","journal-title":"IMA J. Numer. Anal."},{"key":"9800_CR27","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1016\/j.apnum.2006.03.022","volume":"56","author":"EF Toro","year":"2006","unstructured":"Toro, E.F.: MUSTA: a multi-stage numerical flux. Appl. Numer. Math. 56, 1464\u20131479 (2006)","journal-title":"Appl. Numer. Math."},{"key":"9800_CR28","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.jcp.2005.12.012","volume":"216","author":"EF Toro","year":"2006","unstructured":"Toro, E.F., Titarev, V.A.: MUSTA fluxes for systems of conservation laws. J. Comput. Phys. 216, 403\u2013429 (2006)","journal-title":"J. Comput. Phys."},{"key":"9800_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/b79761","volume-title":"Riemann Solvers and Numerical Methods for Fluid Dynamics","author":"EF Toro","year":"2009","unstructured":"Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd edn. Springer, New York (2009)","edition":"3"},{"key":"9800_CR30","doi-asserted-by":"crossref","first-page":"A2072","DOI":"10.1137\/110840832","volume":"34","author":"M Torrilhon","year":"2012","unstructured":"Torrilhon, M.: Krylov-Riemann solver for large hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 34, A2072\u2013A2091 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"9800_CR31","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.jcp.2004.06.015","volume":"201","author":"M Torrilhon","year":"2004","unstructured":"Torrilhon, M., Balsara, D.S.: High order WENO schemes: investigations on non-uniform convergence for MHD Riemann problems. J. Comput. Phys. 201, 586\u2013600 (2004)","journal-title":"J. Comput. Phys."},{"key":"9800_CR32","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/0021-9991(92)90378-C","volume":"102","author":"I Toumi","year":"1992","unstructured":"Toumi, I.: A weak formulation for Roe approximate Riemann solver. J. Comput. Phys. 102, 360\u2013373 (1992)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9800-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9800-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9800-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:45:45Z","timestamp":1559465145000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9800-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,10]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9800"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9800-2","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,10]]}}}