Divergence Free Velocity Interpolation For Surface Marker Tracking
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In the context of multiphase flow simulation, the interface tracking has a crucial role in order to properly preserve the mass of a specific phase and compute all the quantities related to the position of the interface, such as the surface tension. In this work, we exploit a point-wise divergence-free finite element representation of the velocity field to improve the mass conservation features of a surface tracking technique based on the reconstruction of the interface through a best-fit quadratic interpolation of a set of markers. In fact, the divergence-free condition of the velocity is strictly related to the mass conservation and can achieve better results than classic bi-linear or bi-quadratic finite element interpolations. The Raviart-Thomas interpolation guarantees that the reconstruction of the field is appropriately divergence-free in each point of the computational domain, differently from the finite element Lagrangian interpolation that is only divergence-free in the weak form (i.e. when integrated on a cell of the domain). The interface tracking technique adopted in this work is based on the marker technique, through which the surface equation is found as the best-fit quadric approximation of the marker positions that are advected in time through a Runge-Kutta 4th order algorithm. The approach is tested with a set of kinematic examples that stress the advection algorithm due to deformation of the initial surface configuration, and compared to the classical Lagrangian interpolation techniques.
