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

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 conservatively coupled scheme based on standard stabilized linear equal-order finite elements for the Stokes part and vertexcentered 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...

• Type: Journal
• Year: 2016
• Where: JCPHY
• Authors: Christian Waluga, Barbara I. Wohlmuth, Ulrich Rüde
• Keywords: JCPHY 2016