Graduate Seminar "Aktuelle Themen der Numerik"

 

Thursday, Dec 04, 2014, 02:00 pm

Achieving local mass-conservation in coupled flow/transport problems using continuous pressure spaces

Dr. Christian Waluga (TU München)

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 mixed 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 this talk, we shall demonstrate that continuous pressure spaces do not prevent local mass-conservation, but rather require a different viewpoint to understand their conservation properties. We exploit the weak conservation-properties of the continuous pressure schemes to construct local mass-flux corrections on the faces of the barycentric dual of our triangulation. The resulting conservative fluxes can then be either directly used for the assembly of convective terms on the dual skeleton or lifted into Brezzi-Douglas-Marini spaces on the original triangulation. To illustrate the practicability and performance of our approach, we discuss the implementation of the coupling between pressure-stabilized equal-order finite elements and vertex-centered finite volumes in 3D using the hierarchical hybrid grid (HHG) framework.

This is joint work with Björn Gmeiner (FAU Erlangen) and Barbara Wohlmuth (TU München).

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen