{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:32:54Z","timestamp":1787340774376,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100013287","name":"Science Challenge Project","doi-asserted-by":"publisher","award":["TZ2016002"],"award-info":[{"award-number":["TZ2016002"]}],"id":[{"id":"10.13039\/501100013287","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001051"],"award-info":[{"award-number":["12001051"]}],"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":["11971041"],"award-info":[{"award-number":["11971041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure approach with remarkable advantages over the canonical approach. Instead of approximating the flux function, the new approach closes the moment model by approximating the flux gradient. Precisely, we approximate the space derivative of the distribution function by an ansatz which is a weighted polynomial, and the derivative of the closing flux is computed by taking the moments of the ansatz. Consequently, the method provides us an improved framework to derive globally hyperbolic moment models, which preserve all those conservative variables in the low order moments. It is shown that the linearized system at the weight function, which is often the local equilibrium, of the moment model deduced by our new approach is automatically coincided with the system deduced from the classical perturbation theory, which cannot be satisfied by the previous hyperbolic regularization framework. Taking, the Boltzmann equation as an example, the linearlization of the moment model gives the correct Navier--Stokes--Fourier law, which is the same result as that which the Chapman--Enskog expansion gives. Most existing globally hyperbolic moment models are reproduced by our new approach, and several new models are proposed based on this framework.<\/jats:p>","DOI":"10.1137\/21m1396836","type":"journal-article","created":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T10:58:13Z","timestamp":1633345093000},"page":"2153-2179","source":"Crossref","is-referenced-by-count":4,"title":["Direct Flux Gradient Approximation to Moment Closure of Kinetic Equations"],"prefix":"10.1137","volume":"81","author":[{"given":"Ruo","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weiming","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingchao","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2016.9.237"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/41\/013"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/45\/021"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"G. 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