Axisymmetric mass conservative coupling of fluid flow and solute transport
Authors
- Fuhrmann, Jürgen
ORCID: 0000-0003-4432-2434 - Merdon, Christian
ORCID: 0000-0002-3390-2145 - Runge, Daniel
ORCID: 0009-0000-3261-8954
2020 Mathematics Subject Classification
- 76D07 65N30 65N08 35B45
2010 Physics and Astronomy Classification Scheme
- 47.10.ad 47.11.Df.
Keywords
- Transport equation, Stokes equation, cylindrical coordinates, a priori error estimates, maximum principle, mass conservation
DOI
Abstract
This paper is concerned with the physically consistent simulation of fluid flow and transport in complex geometries axisymmetric geometries. In this situation, cylindrical coordinates allow a dimension reduction of the three-dimensional problem to a two-dimensional one. In the three-dimensional setting, a mass conservative discretization can be achieved, e.g. by coupling divergence-free finite element methods for the flow with a conservative finite volume discretization for the transport. A replication of this approach in the reduced two-dimensional formulation with cylindrical coordinates is not straight-forward. Therefore, modifications are suggested that ensure the desired qualitative properties and allow a priori error estimates in suitable weighted Sobolev norms. Several numerical experiments study convergence rates and confirm the theoretical results.
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