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In this work a new model for the analysis of incompressible fluid flows with massive instabilities at different scales is presented. It relies on resolving all the instabilities at all scales without any additional model, i.e. following the Direct Numerical Simulation style. Nevertheless, the computation is carried out at two levels or scales, termed the coarse and the fine. The fine scale simulation is performed on Representative Volume Elements (RVEs) providing the homogenized stress tensor as a function of several dimensionless numbers characterizing the flow. Consequently, the effect of the fine scale instabilities is transferred to the coarse level as a homogenized stress tensor, a procedure inspired by standard multi-scale methods used in solids. The present proposal introduces a new way for the treatment of the flow at the fine scale, simulating not only coarse scale but also the fine scales with all the necessary detail, but without incurring in the excessive computational cost of the classical DNS. Another interesting aspect of the present proposal is the use of a Lagrangian formulation for convecting the eddies simulated on the fine mesh through the coarse domain. Several examples showing the potentiality of this methodology for the simulation of homogeneous flows such are presented.

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Moving liquid-gas interfaces appear frequently in both natural processes and engineering applications. In the case of partially filled tanks, for instance, the accurate description of the free surface transient behavior during transportation or earthquakes is of paramount importance for structural stability analyses. This work presents new experimental data of sloshing at laboratory scale in a vertical cylindrical tank with different filling levels, along with numerical simulations of selected cases using an open source finite volume application. Maximum and minimum experimental wave heights, measured with ultrasonic sensors, are reported for several non-resonant cases during the periodic steady state regime, along with snapshots of a video recorded near-resonance case. For the numerical simulations, a suitable mesh was designed based on a mesh convergence analysis focused on the simulated velocity profiles at the tank wall. A slight nonlinear behavior is detected in the experimental wave patterns, expressed as non-symmetrical minimum and maximum wave heights. The near-resonance case, in turn, shows a highly three-dimensional behavior of the free surface and a rotational effect. The numerical results obtained for the non-resonant cases show good overall agreement with the experiments, although the non-linear behavior is not accurately modelled. The evolution of the highly distorted free surface in the near-resonance case is well captured by the simulation, along with the observed rotational effect.

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