Journal of Scientific Computing

, Volume 77, Issue 3, pp 1424–1443 | Cite as

Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows

  • Karol L. CascavitaEmail author
  • Jérémy Bleyer
  • Xavier Chateau
  • Alexandre Ern


We devise a hybrid low-order method for Bingham pipe flows, where the velocity is discretized by means of one unknown per mesh face and one unknown per mesh cell which can be eliminated locally by static condensation. The main advantages are local conservativity and the possibility to use polygonal/polyhedral meshes. We exploit this feature in the context of adaptive mesh refinement to capture the yield surface by means of local mesh refinement and possible coarsening. We consider the augmented Lagrangian method to solve iteratively the variational inequalities resulting from the discrete Bingham problem, using piecewise constant fields for the auxiliary variable and the associated Lagrange multiplier. Numerical results are presented in pipes with circular and eccentric annulus cross-section for different Bingham numbers.


Hybrid discretization Yield fluids Local mesh refinement Augmented Lagrangian 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University Paris-Est, CERMICS (ENPC)Marne la Vallée Cedex 2France
  2. 2.INRIA ParisParisFrance
  3. 3.NAVIER, UMR 8205, École des Ponts, IFSTTAR, CNRS, UPEChamps-sur-MarneFrance

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