Formulation of Neumann boundary conditions for arbitrary domains

  • Boolakee, Oliver (ETH Zurich)
  • Geier, Martin (TU Braunschweig)
  • De Lorenzis, Laura (TU Braunschweig)

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Recent modeling frameworks to predict the mechanics of additive manufacturing processes involve both fluid and solid mechanics, with the former often described adopting the lattice Boltzmann method. Motivated by the wish to model all physics with the same method, we proposed a novel lattice Boltzmann formulation to solve the equations of linear elastic solids [1]. In comparison to previous attempts in the same direction [2, 3], our approach aims at higher accuracy and efficiency, as well as at retaining the aforementioned benefits of the method while avoiding the recourse to ingredients from the finite difference method. The focus of this study lies on the consistent formulation of Neumann-type boundary conditions within the context of solid mechanics. The goal of the formulation is to achieve second-order accuracy at the boundary using only node-local information. The construction of the required expressions is guided by the asymptotic expansion technique [4, 5]. As a result a systematic procedure to enforce the physical boundary condition is obtained, which could also be applied to different problems solved with the lattice Boltzmann method. The analytically derived expressions are verified by numerical experiments on arbitrary domains with curved boundaries.