{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:35:00Z","timestamp":1787337300260,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>The characteristics\u2010mixed method considers the transport not of a single point or fluid particle, but rather the mass in an entire region of fluid. This mass is transported along the characteristic curves of the hyperbolic part of the transport equation, and the scheme thereby produces very little numerical dispersion, conserves mass locally, and can use long time steps. However, since the shape of a characteristic trace\u2010back region must be approximated in numerical implementation, its volume may be incorrect, resulting in inaccurate concentration densities and, further, inaccurate reaction dynamics. We present a simple modification to the characteristics\u2010mixed method that conserves both mass and volume of the transported fluid regions. Our algorithm also handles boundary conditions through a space\u2010time change of variables in the trace\u2010back routines, which allows the boundary to be treated as if it were interior to the domain. Nearly point sources, such as wells, present special difficulties, since characteristic trace\u2010back curves converge in their vicinity. We also present techniques that allow one to conservatively implement wells. The techniques are illustrated in five numerical examples.<\/jats:p>","DOI":"10.1137\/040621077","type":"journal-article","created":{"date-parts":[[2006,12,11]],"date-time":"2006-12-11T14:43:47Z","timestamp":1165848227000},"page":"2001-2022","source":"Crossref","is-referenced-by-count":38,"title":["A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems"],"prefix":"10.1137","volume":"28","author":[{"given":"Todd","family":"Arbogast","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chieh\u2010Sen","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,12,5]]},"reference":[{"key":"R1","unstructured":"T. Arbogast,\n                      User\u2019s Guide to Parssim1: The Parallel Subsurface Simulator, Single Phase\n                      , Tech. Rep. TICAM Report 98\u201013, The Center for Subsurface Modeling, Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX, May 1998."},{"key":"R2","unstructured":"T. Arbogast, A. Chilakapati, and M. F. Wheeler,\n                      A characteristic\u2010mixed method for contaminant transport and miscible displacement\n                      , in Computational Methods in Water Resources IX, Vol. 1: Numerical Methods in Water Resources, T. F. Russell et al., eds., Computational Mechanics Publications, Southampton, UK, 1992, pp. 77\u201384."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0732017"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994262585"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90065-4"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0309-1708(90)90041-2"},{"key":"R7","unstructured":"A. Chilakapati,\n                      Numerical Simulation of Reactive Flow and Transport through the Subsurface\n                      , Ph.D. thesis, Rice University, Houston, Texas, 1993."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/S0309-1708(98)00036-0"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0730068"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050453"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011551614492"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0719063"},{"key":"R13","unstructured":"R. W. Healy and T. F. Russell,\n                      Treatment of internal sources in the finite\u2010volume ELLAM\n                      , in Computational Methods in Water Resources XIII, Vol. 2, L. R. Bentley, J. F. Sykes, C. A. Brebbia, W. G. Gray, and G. F. Pinder, eds., A. A. Balkema, Rotterdam, 2000, pp. 619\u2013622."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1029\/WR022i011p01597"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"R. J. LeVeque,\n                      Numerical Methods for Conservation Laws\n                      , 2nd ed., Birkh\u00e4user, Basel, 1992.","DOI":"10.1007\/978-3-0348-8629-1"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"R. A. Raviart and J. M. Thomas,\n                      A mixed finite element method for 2nd order elliptic problems\n                      , in Mathematical Aspects of Finite Element Methods, I. Galligani and E. Magenes, eds., Lecture Notes in Math. 606, Springer\u2010Verlag, New York, 1977, pp. 292\u2013315.","DOI":"10.1007\/BFb0064470"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"T. F. Russell and M. F. Wheeler,\n                      Finite element and finite difference methods for continuous flows in porous media\n                      , in The Mathematics of Reservoir Simulation, R. E. Ewing, ed., 1 Frontiers Appl. Math., SIAM, Philadelphia, 1983, pp. 35\u2013106.","DOI":"10.1137\/1.9781611971071.ch2"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(79)90145-1"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"C. D. White and R. N. Horne,\n                      Computing absolute transmissibility in the presence of fine\u2010scale heterogeneity, Paper SPE\n                      16011, in Proceedings, Ninth SPE Symposium on Reservoir Simulation, 1987, pp. 209\u2013220.","DOI":"10.2118\/16011-MS"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/040621077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:27Z","timestamp":1787334927000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/040621077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":19,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/040621077"],"URL":"https:\/\/doi.org\/10.1137\/040621077","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}