Imposing mixed Dirichlet-Neumann-Robin boundary conditions in a level-set framework

Ásdís Helgadóttir, Yen Ting Ng, Chohong Min, Frédéric Gibou

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12 Scopus citations


We consider the Poisson equation with mixed Dirichlet, Neumann and Robin boundary conditions on irregular domains. We describe a straightforward and efficient approach for imposing the mixed boundary conditions using a hybrid finite-volume/finite-difference approach, leveraging on the work of Gibou et al. (2002) [14], Ng et al. (2009) [30] and Papac et al. (2010) [33]. We utilize three different level set functions to represent the irregular boundary at which each of the three different boundary conditions must be imposed; as a consequence, this approach can be applied to moving boundaries. The method is straightforward to implement, produces a symmetric positive definite linear system and second-order accurate solutions in the L-norm in two and three spatial dimensions. Numerical examples illustrate the second-order accuracy and the robustness of the method.

Original languageEnglish
Pages (from-to)68-80
Number of pages13
JournalComputers and Fluids
StatePublished - 22 Oct 2015

Bibliographical note

Funding Information:
The research of Á. Helgadóttir, Y.T. Ng and F. Gibou were supported in part by ONR under grant agreement N00014-11-1-0027 , by the National Science Foundation under grant agreement CHE 1027817 and by the W.M. Keck Foundation . The research of C. Min was supported in part by the Kyung Hee University Research Fund ( KHU-20070608 ) in 2007 and by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-331-C00045).

Publisher Copyright:
© 2015 Elsevier Ltd.


  • Finite difference
  • Level set
  • Mixed boundary conditions


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