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Event Details

  • Monday, May 22, 2017
  • 16:40 - 17:10

A Fully-Coupled Model for the DNS of Particulate Flow

In many applications the simulated fluid incorporates a rather small amount of particles and each single particle needs to be resolved. In biological systems the high viscosity of the surrounding cytosol plays a dominant role since the hydrodynamic interaction between the fluid and the particle serves as dedicated communication pathway within the overall system. So called direct numerical simulation is necessary. We derived a fully coupled and stable method for an appropriate formulation of the interacting forces. Many methods introduce external forces to describe the interaction between fluid and particles. Such an approach typically leads to a saddle point problem. We utilize a finite volume discretization of the Navier-Stokes equations. Its theoretical treatment as a so-called Petrov-Galerkin method enables to develop a fully coupled model, naturally incorporating the particles into the equations. By rigorous extension of the solution space and also the test space of the bilinear operator the internal forces can be formulated in a rather natural way on the basis of the underlying model equations. Our approach leads to an implicit representation of the according forces. The main benefit is the avoidance of a saddle point formulation. Consequently, the solving procedure is conducted in one step and the coupling of the interaction forces can be preserved. Furthermore, in contrast to other approaches, no stabilizing terms need to be introduced to achieve stability: By exploiting the comparability to a finite element method our method can even be proved to be stable. In addition, the immersed boundary is represented as sharp interface in the discrete equations. Second order convergence in space was reached. Finally, the resulting discrete scheme is consistent with the original, unrestricted equations without particles.