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**Viscoelastic mobility problem of a system of particles.**
*(English)*
Zbl 1058.76592

Summary: We present a new implementation of the distributed Lagrange multiplier/fictitious domain (DLM) method by making some modifications over the original algorithm for the Newtonian case developed by R. Glowinski et al. [Int. J. Multiphase Flow 25, 755–794 (1999)], and its extended version for the viscoelastic case by P. Singh et al. [J. Non-Newton. Fluid Mech. 91, 165–188 (2000; Zbl 0972.76080)]. The key modification is to replace a finite element triangulation for the velocity and a “staggered” (twice coarser) triangulation for the pressure with a rectangular discretization for velocity and pressure. The sedimentation of a single circular particle in a Newtonian fluid at different Reynolds numbers, sedimentation of particles in Oldroyd-B fluid, and lateral migration of a single particle in Poiseuille flow of Newtonian fluid are numerically simulated with our code. The results show that the new implementation can give a more accurate prediction of the motion of particles compared to the previous DLM codes, and even to boundary-fitted methods in some cases. The centering of a particle and the well-organized von Kármán vortex street are observed at high Reynolds numbers in our simulation of particle sedimenting in Newtonian fluid. Both results obtained using the DLM method and the spectral element method reveal that the direct contribution of the viscoelastic normal stress to the force on a particle in Oldroyd-B fluid is very important.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76T20 | Suspensions |

76A10 | Viscoelastic fluids |