Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily...

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Published inJournal of computational physics Vol. 321; pp. 512 - 531
Main Authors Adam, A., Pavlidis, D., Percival, J.R., Salinas, P., Xie, Z., Fang, F., Pain, C.C., Muggeridge, A.H., Jackson, M.D.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2016
Subjects
Conservative
Galerkin projection
Interface capturing
Mesh adaptivity
Mesh-to-mesh interpolation
Viscous fingering
Viscous fingering
Mesh-to-mesh interpolation
Galerkin projection
Mesh adaptivity
Interface capturing
Conservative
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Summary:A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.05.058