A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows
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Date
2025-07
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Abstract
We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition
/ Chimera / overset grid meshes. In addition to calculating the velocity and pressure of the fictitious fluid on a fixed background mesh, we solve the incompressible Navier-Stokes equations on body-fitted
submeshes that are attached to moving particles. The submesh velocity and pressure are used to calculate the hydrodynamic forces and torques acting on the particles. The coupling with the background
velocity and pressure is enforced via (i) Robin-type boundary conditions for an Arbitrary-Lagrangian-Eulerian (ALE) formulation of the submesh problems and (ii) a Dirichlet-type distributed interior
penalty term in the weak form of the background mesh problem. The implementation of the weak Dirichlet-Robin coupling is discussed in the context of discrete projection methods. Detailed numerical
studies are performed for standard test problems involving fixed and moving immersed objects. A comparison with fictitious boundary methods illustrates significant gains in the accuracy of drag and lift approximation.
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Keywords
particulate flows, fictitious domains, embedded boundaries, finite element methods, overlapping grids, Chimera domain decomposition, Dirichlet–Robin coupling