{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T11:14:25Z","timestamp":1791458065832,"version":"4.3.4"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100009953","name":"Michigan Technological University","doi-asserted-by":"publisher","award":["1605052"],"award-info":[{"award-number":["1605052"]}],"id":[{"id":"10.13039\/100009953","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571367"],"award-info":[{"award-number":["11571367"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601536"],"award-info":[{"award-number":["11601536"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the $i$th component of the fluid mixture, $c_i$, should be between 0 and 1. However, $c_i$ does not satisfy the maximum principle. Therefore, the numerical techniques introduced in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091--3120] cannot be applied directly. The main idea is to apply the positivity-preserving techniques to both $c_1$ and $c_2$, respectively, and enforce $c_1+c_2=1$ simultaneously to obtain physically relevant approximations. By doing so, we have to treat the time derivative of the pressure $dp\/dt$ as a source in the concentration equation. Moreover, $c_i$'s are not the conservative variables; as a result, the classical bound-preserving limiter in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091--3120] cannot be applied. Therefore, another limiter will be introduced. Numerical experiments will be given to demonstrate the accuracy in the $L^\\infty$-norm and good performance of the numerical technique.<\/jats:p>","DOI":"10.1137\/16m1101313","type":"journal-article","created":{"date-parts":[[2017,9,12]],"date-time":"2017-09-12T10:49:46Z","timestamp":1505213386000},"page":"A1969-A1990","source":"Crossref","is-referenced-by-count":43,"title":["Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media"],"prefix":"10.1137","volume":"39","author":[{"given":"Hui","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/070712079"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-014-9426-y"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/num.20431"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.12.039"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1094942-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.11.021"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.03.019"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9448-0"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1983170302491"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1983170100171"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1983-0717695-3"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2009.12.014"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2009.02.011"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450036757X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.01.090"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-014-4879-y"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.02.041"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2003.11.002"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1002\/num.20684"},{"key":"atypb21","first-page":"28","volume":"2","author":"Ma N.","journal-title":"Internat. 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