文章基本信息

标题：Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model
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作者：Muhammad Rehan Saleem ; Ubaid Ahmed Nisar ; Shamsul Qamar 等
期刊名称：Advances in Mechanical Engineering
印刷版ISSN：1687-8140
电子版ISSN：1687-8140
出版年度：2019
卷号：11
期号：9
页码：1-16
DOI：10.1177/1687814019874908
出版社：Sage Publications Ltd.
摘要：This article deals with the numerical study of two-phase shallow flow model describing the mixture of fluid and solid granular particles. The model under investigation consists of coupled mass and momentum equations for solid granular material and fluid particles through non-conservative momentum exchange terms. The non-conservativity of model equations poses major challenges for any numerical scheme, such as well balancing, positivity preservation, accurate approximation of non-conservative terms, and achievement of steady-state conditions. Thus, in order to approximate the present model an accurate, well-balanced, robust, and efficient numerical scheme is required. For this purpose, in this article, Runge–Kutta discontinuous Galerkin method is applied successfully for the first time to solve the model equations. Several test problems are also carried out to check the performance and accuracy of our proposed numerical method. To compare the results, the same model is solved by staggered central Nessyahu–Tadmor scheme. A good comparison is found between two schemes, but the results obtained by Runge–Kutta discontinuous Galerkin scheme are found superior over the central Nessyahu–Tadmor scheme.
其他关键词：Two-phase shallow flow model ; incompressible flow ; non-conservative hyperbolic system ; discontinuous Galerkin method ; central Nessyahu–Tadmor scheme