Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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• 作者：Christian Waluga^a ; ^{waluga@ma.tum.de" class="auth_mail" title="E-mail the corresponding author} ; Barbara Wohlmuth^a ; Ulrich Rü ; de^b
• 关键词：Finite element method ; Finite volume method ; Flow/transport coupling ; Local mass-conservation ; Incompressible flow ; Unstructured meshes
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：319-332
• 全文大小：3127 K

文摘

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilized linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.