A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows

TL;DR

This paper presents a novel multimesh finite element method for simulating incompressible particulate flows, combining overlapping domain decomposition with weak Dirichlet-Robin coupling to improve accuracy in hydrodynamic force calculations.

Contribution

It introduces a new Chimera domain decomposition approach with weak Dirichlet-Robin coupling for enhanced particulate flow simulations, integrating ALE formulation and finite element discretization.

Findings

Significant accuracy improvements in drag and lift calculations.

Effective coupling of background and submesh solutions via Robin and Dirichlet conditions.

Validation on standard test problems with fixed and moving particles.

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 and finite element discretizations. Detailed numerical studies are performed for standard test problems involving fixed and moving immersed objects. A comparison of Chimera results with those produced by fictitious boundary methods illustrates significant gains in the accuracy of drag and lift approximations.