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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11 Scopus citations

Abstract

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
Volume121
DOIs
StatePublished - 22 Oct 2015

Keywords

  • Finite difference
  • Level set
  • Mixed boundary conditions

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