{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T04:13:29Z","timestamp":1751516009920,"version":"3.41.0"},"reference-count":66,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFA1004500"],"award-info":[{"award-number":["2022YFA1004500"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92270112"],"award-info":[{"award-number":["92270112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2023J02003"],"award-info":[{"award-number":["2023J02003"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In [G. Huang, S. Boscarino and T. Xiong,\nHigh order asymptotic preserving and well-balanced schemes for the shallow water equations with source terms,\nCommun. Comput. Phys. 35 2024, 5, 1229\u20131262], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (SWEs) with bottom topography and Manning friction, utilizing a penalization technique inspired by [S. Boscarino, P. G. LeFloch and G. Russo,\nHigh-order asymptotic-preserving methods for fully nonlinear relaxation problems,\nSIAM J. Sci. Comput. 36 2014, 2, A377\u2013A395].\nAlthough the added weighted diffusive term enhanced stability, it increased computational cost and slowed down the convergence rate in the intermediate regime between convection and diffusion.\nIn this paper, we extend our previous study by removing the penalization while preserving the AP property.\nTo achieve this, we employ a high order semi-implicit implicit-explicit Runge\u2013Kutta (SI-IMEX-RK) time discretization, coupled with high-order WENO reconstructions for first-order derivatives and central difference schemes for second-order spatial derivatives. This combination yields a class of fully high-order schemes.\nTheoretical analysis and numerical experiments demonstrate that the proposed schemes retain AP, asymptotically accurate and well-balanced properties, while offering higher computational efficiency compared to our previous scheme in Huang, Boscarino and Xiong (2024), especially in the intermediate regime between convection and diffusion.\nMoreover, treating the momentum in the friction terms implicitly is essential for preserving the AP property; otherwise, the scheme fails to converge to the limiting equations. This indicates that implicit treatment of Manning friction is necessary for the stability of the method.<\/jats:p>","DOI":"10.1515\/cmam-2024-0186","type":"journal-article","created":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T10:01:19Z","timestamp":1746352879000},"page":"619-641","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic Preserving Semi-Implicit Scheme for the Shallow Water Equations with Non-Flat Bottom Topography and Manning Friction Term"],"prefix":"10.1515","volume":"25","author":[{"given":"Guanlan","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , Key Laboratory of Analytical Mathematics and Applications (Ministry of Education), Fujian Key Laboratory of Analytical Mathematics and Applications (FJKLAMA), Center for Applied Mathematics of Fujian Province (FJNU) , Fujian Normal University , Fuzhou, Fujian , 350117 , P. R. China"}]},{"given":"Sebastiano","family":"Boscarino","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science , University of Catania , Catania 95125 , Italy"}]},{"given":"Tao","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , 12652 University of Science and Technology of China , Hefei, Anhui , 230026 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2025,4,30]]},"reference":[{"key":"2025070217063890661_j_cmam-2024-0186_ref_001","doi-asserted-by":"crossref","unstructured":"F.  Andreu, J. M.  Maz\u00f3n, S.  Segura de Le\u00f3n and J.  Toledo,\nExistence and uniqueness for a degenerate parabolic equation with \n                  \n                     \n                        \n                           L\n                           1\n                        \n                     \n                     \n                     L^{1}\n                  \n               -data,\nTrans. Amer. Math. Soc. 351 (1999), no. 1, 285\u2013306.","DOI":"10.1090\/S0002-9947-99-01981-9"},{"key":"2025070217063890661_j_cmam-2024-0186_ref_002","doi-asserted-by":"crossref","unstructured":"A.  Bermudez and M. E.  Vazquez,\nUpwind methods for hyperbolic conservation laws with source terms,\nComput. & Fluids 23 (1994), no. 8, 1049\u20131071.","DOI":"10.1016\/0045-7930(94)90004-3"},{"key":"2025070217063890661_j_cmam-2024-0186_ref_003","doi-asserted-by":"crossref","unstructured":"G.  Bispen, K. R.  Arun, M.  Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1 and S.  Noelle,\nIMEX large time step finite volume methods for low Froude number shallow water flows,\nCommun. Comput. Phys. 16 (2014), no. 2, 307\u2013347.","DOI":"10.4208\/cicp.040413.160114a"},{"key":"2025070217063890661_j_cmam-2024-0186_ref_004","doi-asserted-by":"crossref","unstructured":"G.  Bispen, M.  Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1 and L.  Yelash,\nAsymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation,\nJ. Comput. Phys. 335 (2017), 222\u2013248.","DOI":"10.1016\/j.jcp.2017.01.020"},{"key":"2025070217063890661_j_cmam-2024-0186_ref_005","doi-asserted-by":"crossref","unstructured":"S.  Boscarino, F.  Filbet and G.  Russo,\nHigh order semi-implicit schemes for time dependent partial differential equations,\nJ. Sci. Comput. 68 (2016), no. 3, 975\u20131001.","DOI":"10.1007\/s10915-016-0168-y"},{"key":"2025070217063890661_j_cmam-2024-0186_ref_006","doi-asserted-by":"crossref","unstructured":"S.  Boscarino, P. G.  LeFloch and G.  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