WIAS Preprint No. 2543, (2018)

Gradient structures for flows of concentrated suspensions


Authors

  • Peschka, Dirk
    ORCID: 0000-0002-3047-1140
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X
  • Ahnert, Tobias
  • Münch, Andreas
  • Wagner, Barbara
    ORCID: 0000-0001-8306-3645

2010 Mathematics Subject Classification

  • 76T20 35R35 49J40 76M30

Keywords

  • Two-phase suspension flow, free boundary problem, non-smooth dissipation, generalized gradient structure based on low maps

DOI

10.20347/WIAS.PREPRINT.2543

Abstract

In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth two-homogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows

Appeared in

  • Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 295--318, DOI 10.1007/978-3-030-33116-0 .

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