5,740 research outputs found
On the modelling of isothermal gas flows at the microscale
This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.
Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers
The usefulness of higher-order constitutive relations for describing the Knudsen layer
The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight
Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows
In hypersonic aerodynamics and microflow device design, the momentum and energy fluxes to solid surfaces are often of critical importance. However, these depend on the characteristics of the Knudsen layer - the region of local non-equilibrium existing up to one or two molecular mean free paths from the wall in any gas flow near a surface. While the Knudsen layer has been investigated extensively using kinetic theory, the ability to capture it within a continuum-fluid formulation (in conjunction with slip boundary conditions) suitable for current computational fluid dynamics toolboxes would offer distinct and practical computational advantages
Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars
Determining accurate and precise stellar ages is a major problem in
astrophysics. These determinations are either obtained through empirical
relations or model-dependent approaches. Currently, seismic modelling is one of
the best ways of providing accurate ages. However, current methods are affected
by simplifying assumptions concerning mixing processes. In this context,
providing new structural indicators which are less model-dependent and more
sensitive to such processes is crucial. We build a new indicator for core
conditions on the main sequence, which should be more sensitive to structural
differences and applicable to older stars than the indicator t presented in a
previous paper. We also wish to analyse the importance of the number and type
of modes for the inversion, as well as the impact of various constraints and
levels of accuracy in the forward modelling process that is used to obtain
reference models for the inversion. First, we present a method to obtain new
structural kernels and use them to build an indicator of central conditions in
stars and test it for various effects including atomic diffusion, various
initial helium abundances and metallicities, following the seismic inversion
method presented in our previous paper. We then study its accuracy for 7
different pulsation spectra including those of 16CygA and 16CygB and analyse
its dependence on the reference model by using different constraints and levels
of accuracy for its selection We observe that the inversion of the new
indicator using the SOLA method provides a good diagnostic for additional
mixing processes in central regions of stars. Its sensitivity allows us to test
for diffusive processes and chemical composition mismatch. We also observe that
octupole modes can improve the accuracy of the results, as well as modes of low
radial order.Comment: Accepted for publication in Astronomy and Astrophysic
Constraints on the structure of 16 Cyg A and 16 Cyg B using inversion techniques
Constraining mixing processes and chemical composition is a central problem
in stellar physics as their impact on stellar age determinations leads to
biases in our studies of stellar evolution, galactic history and exoplanetary
systems. In two previous papers, we showed how seismic inversion techniques
could offer strong constraints on such processes by pointing out weaknesses in
theoretical models. We now apply our technique to the solar analogues 16CygA
and 16CygB, being amongst the best targets in the Kepler field to test the
diagnostic potential of seismic inversions. The combination of various seismic
indicators helps to provide more constrained and accurate fundamendal
parameters for these stars. We use the latest seismic, spectroscopic and
interferometric observational constraints in the litterature for this system to
determine reference models independently for both stars. We carry out seismic
inversions of the acoustic radius, the mean density and a core conditions
indicator. We note that a degeneracy exists for the reference models. Namely,
changing the diffusion coefficient or the chemical composition within the
observational values leads to 5% changes in mass, 3% changes in radius and up
to 8% changes in age. We use acoustic radius and mean density inversions to
improve our reference models then carry out inversions for a core conditions
indicator. Thanks to its sensitivity to microscopic diffusion and chemical
composition mismatches, we are able to reduce the mass dispersion to 2%, namely
[0.96, 1.0] M_sun, the radius dispersion to 1%, namely [1.188, 1.200] R_sun and
the age dispersion to 3%, namely [7.0, 7.4] Gy, for 16CygA. For 16CygB, we can
check the consistency of the models but not reduce independently the age
dispersion. Nonetheless, assuming consistency with the age of 16CygA helps to
further constrain its mass and radius.Comment: Submitted to Astronomy and Astrophysic
The FADE mass-stat:A technique for inserting or deleting particles in molecular dynamics simulations
The emergence of new applications of molecular dynamics (MD) simulation calls for the development of mass-statting procedures that insert or delete particles on-the-fly. In this paper we present a new mass-stat which we term FADE, because it gradually “fades-in” (inserts) or “fades-out” (deletes) molecules over a short relaxation period within a MD simulation. FADE applies a time-weighted relaxation to the intermolecular pair forces between the inserting/deleting molecule and any neighbouring molecules. The weighting function we propose in this paper is a piece-wise polynomial that can be described entirely by two parameters: the relaxation time scale and the order of the polynomial. FADE inherently conserves overall system momentum independent of the form of the weighting function. We demonstrate various simulations of insertions of atomic argon, polyatomic TIP4P water, polymer strands, and C60 Buckminsterfullerene molecules. We propose FADE parameters and a maximum density variation per insertion-instance that restricts spurious potential energy changes entering the system within desired tolerances. We also demonstrate in this paper that FADE compares very well to an existing insertion algorithm called USHER, in terms of accuracy, insertion rate (in dense fluids), and computational efficiency. The USHER algorithm is applicable to monatomic and water molecules only, but we demonstrate that FADE can be generally applied to various forms and sizes of molecules, such as polymeric molecules of long aspect ratio, and spherical carbon fullerenes with hollow interiors
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