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We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection–diffusion problem within a more general Friedrichs system framework. With carefully constructed numerical traces, we introduce two distinct stabilization parameters: τ t for the tangential trace and τ n for the normal trace. These parameters are tailored to satisfy different requirements, ensuring the stability and convergence of the method. Furthermore, we incorporate a weight function to facilitate the establishment of stability conditions. We also investigate an elementwise postprocessing technique that proves to be effective for both two-dimensional and three-dimensional problems in terms of broken H (curl) semi-norm accuracy improvement. Extensive numerical examples are presented to showcase the performance and effectiveness of the HDG method and the postprocessing techniques. [ABSTRACT FROM AUTHOR]

The deposition of aerosol particles from a Stokes flow in filters composed of nanofibers has been considered at Knudsen numbers ∼ 1. The efficiency of particle collection by model filters with 2D and 3D structures has been determined by numerical simulation as depending on particle radius , filter parameters (nanofiber radius , packing density , and filter thickness), and filtration conditions taking into account the gas slip at the fibers. It has been shown that the efficiencies of particle collection by nanofibers in model 2D and 3D filters are almost equal at the same low packing density < 0.02. It has been found that the dependence of the penetration of particles on their radius at a constant velocity on the order of several centimeters per second and at ∼ 1 passes through a maximum, which corresponds to particle radius . The calculated sizes of the most penetrating particles agree with experimental data. The results obtained will be used when selecting aerosols for testing nanofibrous filters. [ABSTRACT FROM AUTHOR]

The collection of aerosol nanoparticles by filters composed of nanofibers has been theoretically investigated. The convective diffusion deposition of point particles from a Stokes flow in model filters with an ordered structure has been calculated taking into account the effect of gas slip at the fibers. It has been shown that, at small Peclet numbers (), the efficiency of diffusion collection of particles by a fiber does not depend on the Knudsen number (), while, at large Peclet numbers ( ⪢ 1), it varies from at = 0 to at The applicability regions have been determined for the equations used to calculate nanoaerosol collection efficiency. The calculation results have been employed to derive approximation formulas for the collection efficiency within ranges of = 0.1−1000 and [ABSTRACT FROM AUTHOR]

The objective of this experimental investigation is to characterize the gas–surface interaction under different flow conditions. Therefore, the mass flow rates driven by a pressure gradient under isothermal conditions and by only a temperature gradient under constant pressure conditions are measured in the same microchannel for five different gases: helium, neon, nitrogen, argon and krypton. The pressure driven experiments are carried out in the hydrodynamic and slip flow regimes, $0.0016 , while the temperature driven experiments in the slip and transitional flow regimes have $0.05. Using a previously developed methodology, the velocity and thermal slip coefficients are derived from the measured mass flow rates. By adopting the classical Maxwell boundary condition, the accommodation coefficients are found to be very different for both types of flows, with a significantly lower value for polyatomic nitrogen in the case of temperature gradient driven flows. An attempt to calculate the tangential momentum and normal energy accommodation coefficients in the frame of the Cercignani–Lampis model was successful only for the tangential momentum accommodation coefficient, which was found to be very close to that derived with the Maxwell model. However, it was not possible to obtain the values of the normal energy accommodation coefficient due to a lack of numerical results which connect the thermal slip and normal energy accommodation coefficients for very low values of the latter. [ABSTRACT FROM AUTHOR]

We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples. [ABSTRACT FROM AUTHOR]

Practical multibody models are typically composed by a set of bodies (rigid or deformable) linked by joints, represented by constraint equations, and in many cases are subject to potential forces. Thus, a proper formulation of these constraints and forces is an essential aspect in the numerical analysis of their dynamics. On the other hand, geometric integrators are particular time-stepping schemes that have been successfully employed during the last decades in many applications, including multibody systems. One category is the so-called energy-momentum (EM) schemes that exhibit excellent stability and physical accuracy, conserving the discrete energy in conservative systems and preserving possible symmetries related with the conservation of linear and angular momenta. The use of the discrete derivative concept greatly systematizes their formulation, but its particular expression is not unique. This paper discusses the properties of several discrete derivative formulas proposed in the literature for models possessing finite-dimensional and linear configuration spaces, showing that not all of them lead to proper EM schemes. Some formulas, when applied to constraints or potentials endowed with certain symmetries (associated with the conservation of linear and angular momenta, found in many common practical systems), may produce numerical results that conserves the energy but violates the symmetries, introducing numerical instabilities and/or producing unphysical motions. This fact, surprisingly overlooked by many authors, is carefully analyzed and illustrated with several numerical experiments related with the dynamics of representative multibody systems. [ABSTRACT FROM AUTHOR]

This review assesses the current state of understanding of the calculation of the rate of flow of gases, vapours and liquids confined in channels, in porous media and in permeable materials with an emphasis on the flow of water and its vapour. One motivation is to investigate the relation between the permeation rate of moisture and that of a noncondensable test gas such as helium, another is to assist in unifying theory and experiment across disparate fields. Available theories of single component ideal gas flows in channels of defined geometry (cylindrical, rectangular and elliptical) are described and their predictions compared with measurement over a wide range of conditions defined by the Knudsen number. Theory for two phase flows is assembled in order to understand the behaviour of four standard water leak configurations: vapour, slug, Washburn and liquid flow, distinguished by the number and location of phase boundaries (menisci). Air may or may not be present as a background gas. Slip length is an important parameter that greatly affects leak rates. Measurements of water vapour flows confirm that water vapour shows ideal gas behaviour. Results on carbon nanotubes show that smooth walls may lead to anomalously high slip lengths arising from the properties of ‘confined’ water. In porous media, behaviour can be matched to the four standard leaks. Traditional membrane permeation models consider that the permeant dissolves, diffuses and evaporates at the outlet side, ideas we align with those from channel flow. Recent results on graphite oxide membranes show examples where helium which does not permeate while at the same time moisture is almost unimpeded, again a result of confined water. We conclude that while there is no a priori relation between a noncondensable gas flow and a moisture flow, measurements using helium will give results within two orders of magnitude of the moisture flow rate, except in the case where there is anomalous slip or confined water, when moisture specific measurements are essential. [ABSTRACT FROM AUTHOR]