{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:29Z","timestamp":1787337269826,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>This paper presents a new type of second-order scheme for solving the system of Euler equations, which combines the Runge--Kutta discontinuous Galerkin (RKDG) finite element method and the Bhatnagar--Gross--Krook (BGK) scheme. We first discretize the Euler equations in space with the DG method, and then the resulting system will be discretized using an RK method. Finally, a second-order BGK method is used to construct the numerical flux. The proposed scheme keeps the main advantages of the DG finite element method, including its flexibility in handling irregular solution domains and in parallelization. Moreover, with the BGK approach the proposed schemes avoid using Riemann solvers. The efficiency and effectiveness of the proposed method are illustrated by several numerical examples in one- and two-dimensional spaces.<\/jats:p>","DOI":"10.1137\/040618783","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T16:45:19Z","timestamp":1202316319000},"page":"805-831","source":"Crossref","is-referenced-by-count":2,"title":["RKDG Finite Element Method Combined with BGK Scheme for Solving Fluid Dynamics System"],"prefix":"10.1137","volume":"28","author":[{"given":"Qingfang","family":"Dai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xijun","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5720"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1063\/1.869719"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90136-5"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90031-3"},{"key":"R5","first-page":"411","volume":"52","author":"Cockburn Bernardo","year":"1989","journal-title":"Math. 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