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The implicit midpoint time-integration technique is applied to the stochastic Landau-Lifshitz-Gilbert (LLG) equation. The numerical scheme converges to the Stratonovich solution in the limit of vanishing time step. It preserves the magnetization magnitude and the main energy balance properties of the LLG equation independently of the time step. The numerical technique is then applied to the study of superparamagnetic state in a small spheroidal particle, and the numerical results are compared with the theory

A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier-Stokes equations is reported. A general triple splitting of the nonlinear convective terms is considered, and energy-preserving formulations are fully characterized by deriving a two-parameter family of split forms. Previously developed formulations reported in literature are shown to be particular members of this family; novel splittings are introduced and discussed as well. Furthermore, the conservation properties yielded by different choices for the energy equation (i.e. total and internal energy, entropy) are analyzed thoroughly. It is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family. Local conservation of primary invariants, which is a fundamental property to build high-fidelity shock-capturing methods, is also discussed in the paper. Numerical tests performed for the Taylor-Green Vortex at zero viscosity fully confirm the theoretical findings, and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results.

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Numerical simulations of early and intermediate instants of a plane two-dimensional drop impact on a pre-existing thin film of the same liquid are performed. The evolution of the phenomenon is analyzed by solving the free-surface Navier-Stokes equations by means of a Volume of Fluid (VOF) method. Viscous, inertial and surface tension forces are taken into account; gravity is neglected. The so-called splashing regime is emphasised, where the emergence of an initial horizontal ejecta sheet is followed by the formation of an almost vertical lamella sheet, which is the planar counterpart of the well known splashing-crown of spherical geometry. Overall velocity and pressure fields as well as detailed interface shapes are presented, and several insights on the relevant scaling laws are furnished. In the ejecta sheet (jet) regime a major result is the finding of a deviation from the standard square root behavior for the dependence on time of the contact length of sheet first emergence, which is proved to be crucial in the subsequent original application of the potential theory of Howison et al. [J. Fluid Mech., 542, 1 (2005)]. In the lamella sheet regime, the outwards expansion of its base is discussed in connection with the theory of the formation of a kinematic discontinuity within the underneath film of Yarin and Weiss [J. Fluid Mech., 283, 141 (1995)]. Analogies between planar and axysymmetric configurations are discussed

In the last decades, Synthetic jet actuators have gained much interest among the flow control techniques due to their short response time, high jet velocity and absence of traditional piping, which matches the requirements of reduced size and low weight. A synthetic jet is generated by the diaphragm oscillation (generally driven by a piezoelectric element) in a relatively small cavity, producing periodic cavity pressure variations associated with cavity volume changes. The pressured air exhausts through an orifice, converting diaphragm electrodynamic energy into jet kinetic energy. This review paper considers the development of various Lumped-Element Models (LEMs) as practical tools to design and manufacture the actuators. LEMs can quickly predict device performances such as the frequency response in terms of diaphragm displacement, cavity pressure and jet velocity, as well as the efficiency of energy conversion of input Joule power into useful kinetic power of air jet. The actuator performance is also analyzed by varying typical geometric parameters such as cavity height and orifice diameter and length, through a suited dimensionless form of the governing equations. A comprehensive and detailed physical modeling aimed to evaluate the device efficiency is introduced, shedding light on the different stages involved in the process. Overall, the influence of the coupling degree of the two oscillators, the diaphragm and the Helmholtz frequency, on the device performance is discussed throughout the paper.

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