We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations along the trajectory of material elements in a moving grid and a reconstruction of the fields in a reference regular mesh using a non-linear mapping and adaptive moment-preserving interpolations. The non-linear mapping allows for the arbitrary deformation of material elements. Additionally, interpolations can represent discontinuous fields using adaptive-order interpolation near jumps detected with a slope-limiter function. Due to the large number of operations during the interpolations, a serial implementation of this scheme is computationally expensive. The scheme has been accelerated in many-core parallel architectures using a thread per grid node and parallel data gathers. We present a series of tests that prove the scheme to be an attractive option for simulating advection equations in multi-dimensions with high accuracy.

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker-Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.Comment: To be published in Physica A (16 pages, 2 figures

A particle with a density slightly larger than that of the fluid in which it is immersed will sediment. However, if the particle's temperature is higher than that of the fluid, the terminal velocity of sedimentation will be smaller and can even change sign. When the terminal velocity is zero we say there is thermal levitation. Thermal levitation can also occur when the density and temperature of the particle are smaller than those of the fluid. Using a two-component thermal lattice Boltzmann equation method, we study this phenomenon and show it can be stable or unstable.

The two dimensional incompressible viscous flow past a flapping foil immersed in a uniform stream is studied numerically. Numerical simulations were performed using a Lattice-Boltzmann model for moderate Reynolds numbers. The computation of the hydrodynamic force on the foil is related to the the wake structure. In particular, when the foil's centre of mass is fixed in space, numerical results suggest a relation between drag coefficient behaviour and the flapping frequency which determines the transition from the von Kármán (vKm) to the inverted von Kármán wake. Beyond the inverted vKm transition the foil was released. Upstream swimming was observed at high enough flapping frequencies. Computed hydrodynamic forces suggest the propulsion mechanism for the swimming foil.arXiv:1608.03618v1 [physics.flu-dyn]

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