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**Modelling Rayleigh-Taylor instability of a sedimenting suspension of several thousand circular particles in a direct numerical simulation.**
*(English)*
Zbl 0985.76031

Summary: We study the sedimentation of several thousand circular particles in two dimensions using the method of distributed Lagrange multipliers for solid-liquid flow. The simulation gives rise to fingering which resembles Rayleigh-Taylor instabilities. The waves have a well-defined wavelength and growth rate which can be modelled as a conventional Rayleigh-Taylor instability of heavy fluid above light. The heavy fluid is modelled as a composite solid-liquid fluid with an effective composite density and viscosity. Surface tension cannot enter this problem, and the characteristic short-wave instability is regularized by the viscosity of the solid-liquid dispersion. The dynamics of Rayleigh-Taylor instability is studied using viscous potential flow, and an exact solution is obtained.

### MSC:

76E17 | Interfacial stability and instability in hydrodynamic stability |

76T20 | Suspensions |

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