An interface-fitted subspace projection method for finite element simulations of participate flows

摘要

A novel finite element method for the direct numerical simulation of particles in a Newtonian carrier fluid is presented. The proposed method is based on a fictitious or one-domain formulation and a subspace projection method to account for the rigid body motion of the particles. Underlying equations are posed in an ALE (arbitrary Lagrangian-Eulerian) formulation, allowing for moving computational meshes. The mesh is adapted to the particles by a novel mesh smoothing approach, guaranteeing both mesh optimality and a sharp representation of the particles' boundaries. We show that by using quadratic Taylor-Hood finite elements for the discretization of the Navier-Stokes equations and isoparametric elements to represent the geometry, second order convergence with respect to the energy norm can be achieved (as opposed to a sharp h~(1/2) result which holds if no mesh adaptation is performed). We present numerical examples in 2d confirming the theoretical convergence results. Furthermore, we validate the approach by simulating the sedimentation process of a single particle and show the potential of the method by simulating a lid-driven cavity flow with 100 particles.