Mass-corrections for the conservative coupling of flow and transport on collocated meshes
Waluga C, Wohlmuth BI, Rüde U (2016)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: Elsevier
Book Volume: 305
Pages Range: 319-332
Article Number: 043302
URI: http://journals.aps.org/pre/pdf/10.1103/PhysRevE.93.043302
DOI: 10.1016/j.jcp.2015.10.044
Abstract
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. (C) 2015 Elsevier Inc. All rights reserved.
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APA:
Waluga, C., Wohlmuth, B.I., & Rüde, U. (2016). Mass-corrections for the conservative coupling of flow and transport on collocated meshes. Journal of Computational Physics, 305, 319-332. https://doi.org/10.1016/j.jcp.2015.10.044
MLA:
Waluga, Christian, B. I. Wohlmuth, and Ulrich Rüde. "Mass-corrections for the conservative coupling of flow and transport on collocated meshes." Journal of Computational Physics 305 (2016): 319-332.
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