Choice Of Numerical Parameters Research Articles

A linear stability analysis of compressible hybrid lattice Boltzmann methods

An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite difference (FD) schemes solve an energy equation. Both systems are coupled with each other thanks to an ideal gas equation of state. This work aims at answering some questions regarding the numerical stability of such models, which strongly depends on the choice of numerical parameters. To this extent, several one- and two-dimensional HLBM classes based on different energy variables, formulations (primitive or conservative), collision terms and numerical schemes are scrutinized. Once appropriate corrective terms introduced, it is shown that all continuous HLBM classes recover the Navier-Stokes-Fourier behavior in the linear approximation. However, striking differences arise between HLBM classes when their discrete counterparts are analyzed. Multiple instability mechanisms arising at relatively high Mach number are pointed out and two exhaustive stabilization strategies are introduced: (1) decreasing the time step by changing the reference temperature Tr and (2) introducing a controllable numerical dissipation σ via the collision operator. A complete parametric study reveals that only HLBM classes based on the primitive and conservative entropy equations are found usable for compressible applications. Finally, an innovative study of the macroscopic modal composition of the entropy classes is conducted. Through this study, two original phenomena, referred to as shear-to-entropy and entropy-to-shear transfers, are highlighted and confirmed on standard two-dimensional test cases.

Numerical quadrature in the Brillouin zone for periodic Schrödinger operators

As a consequence of Bloch's theorem, the numerical computation of the fermionic ground state density matrices and energies of periodic Schrodinger operators involves integrals over the Brillouin zone. These integrals are difficult to compute numerically in metals due to discontinuities in the integrand. We perform an error analysis of several widely-used quadrature rules and smearing methods for Brillouin zone integration. We precisely identify the assumptions implicit in these methods and rigorously prove error bounds. Numerical results for two-dimensional periodic systems are also provided. Our results shed light on the properties of these numerical schemes, and provide guidance as to the appropriate choice of numerical parameters.

Experimental Validation of Numerical Simulations: A Comparison of Computational Fluid Dynamics and the Oil Film Method

Today Computational Fluid Dynamics (CFD) is used for simulating flow in many applications. The quality of the results, however, depends on various factors, like grid quality, boundary conditions and the computational model of the fluid. For this reason, it is important to validate the performed computation with experimental results. In this work, a comparison of numerical simulation with the oil film method was performed for two cardiovascular applications. The investigations were conducted at various geometries, such as a bended cannula tubing, an impeller of a magnetically levitated rotary blood pump and tips of inflow cannulas. The oil film for the experimental validation was composed of black oil color and varnish. In the numerical simulation, color abrasion was displayed with a special post-processing tool by means of wall-attached pathlines. With the proper choice of numerical parameters, the computer simulations and the oil film method demonstrated good correlation. Improper generation of the simulation grid did lead to divergent results between the numerical simulation and the experiment. For the pump impeller as well as for the inflow cannulas, the calculation and the experiment showed similar flow patterns with backflow and stall zones. The oil film method represents a fast and simple approach to help validate numerical simulations of fluid flow. The experimentally generated near wall flow patterns can be easily compared with the solution of the CFD analysis.

On a method for direct numerical simulation of shear layer/compression wave interaction for aeroacoustic investigations

Direct numerical simulation (DNS) of a spatially developing mixing layer was performed. The compressible three-dimensional Navier–Stokes equations were solved for pressure, velocities and entropy for this flow using a compact finite-difference scheme of sixth-order accuracy in space, combined with Runge–Kutta three-step time advancement. On one of the transverse boundaries of the box-shaped domain, a compression wave profile was imposed in pressure and velocity components via a wave decomposition of the governing equations, in order to study the interaction of an isolated weak shock wave entering the domain with the mixed subsonic/supersonic shear layer. This flow situation is found along the shear layer of supersonic, imperfectly expanded jets containing a shock cell structure. In the present work, an isolated compression–expansion structure constitutes the model problem. The domain setup and the boundary conditions were chosen such as to allow analysis of the sound field generated by the turbulent flow and the shock–turbulence interaction. The numerical method used to impose the boundary conditions and solve the compressible Navier–Stokes equations, and the choice of numerical parameters, are described in detail. Some results on the two-dimensional and three-dimensional flow field computed are presented as well.

On the phase behavior of blends of polymers and nematic liquid crystals

The phase behavior of mixtures of polymers and nematic liquid crystals (LC) is investigated. Two types of systems are examined. The first one deals with blends in which the polymer is made of linear chains. In this case, a systematic study of the effects of various parameters on the phase diagrams is performed. In particular, it is shown how increasing the polymer size and/or the LC molecule size increases the miscibility gap of the mixture. It also reduces the region where a single nematic phase is observed in the presence of a tiny amount of polymer. Likewise, the relative effects of the isotropic and the nematic interaction parameters on the phase diagrams are examined. The second part of this investigation deals with blends involving crosslinked polymers. Here, substantial differences are observed as compared to the case where the polymer components are made of linear chains. These differences are illustrated by showing the phase diagrams in similar conditions for both blends. Unlike the case of a linear polymer matrix, it is observed that the single nematic phase and the nematic-isotropic spinodal branches are absent from the phase diagram of crosslinked polymers. This results into significant distortions of the phase diagram. In order to highlight all these effects, examples representing hypothetical blends are considered. These examples are chosen for illustration of the results in which the choice of numerical parameters is made consistently with the existing values in the literature which makes comparison with published data possible.

On the phase behavior of blends of polymers and nematic liquid crystals

The phase behavior of mixtures of polymers and nematic liquid crystals (LC) is investigated. Two types of systems are examined. The first one deals with blends in which the polymer is made of linear chains. In this case, a systematic study of the effects of various parameters on the phase diagrams is performed. In particular, it is shown how increasing the polymer size and/or the LC molecule size increases the miscibility gap of the mixture. It also reduces the region where a single nematic phase is observed in the presence of a tiny amount of polymer. Likewise, the relative effects of the isotropic and the nematic interaction parameters on the phase diagrams are examined. The second part of this investigation deals with blends involving crosslinked polymers. Here, substantial differences are observed as compared to the case where the polymer components are made of linear chains. These differences are illustrated by showing the phase diagrams in similar conditions for both blends. Unlike the case of a linear polymer matrix, it is observed that the single nematic phase and the nematic-isotropic spinodal branches are absent from the phase diagram of crosslinked polymers. This results into significant distortions of the phase diagram. In order to highlight all these effects, examples representing hypothetical blends are considered. These examples are chosen for illustration of the results in which the choice of numerical parameters is made consistently with the existing values in the literature which makes comparison with published data possible.

Discrete vortex model of flow over a square cylinder

Abstract The discrete vortex method (DVM) is used to numerically study the velocity field in the near wake of a 2-D cylinder of square cross-section. Vortex panels are used to model the cylinder surface, at which a no-penetration boundary condition was imposed. The DVM uses a series of individual vortex elements to model the separated shear layers of the cylinder. The discrete-vortex elements interact to form clusters in the wake region, which represent the larger vortical structures present in such flows. By careful choice of numerical parameters, good agreement is obtained with experimental measurements for the mean and fluctuating velocity fields in the near-wake region. The method is especially effective in modelling the unsteady, quasi-periodic motions associated with the large-scale vortex structures in the wake.

The electronic structure and magnetic properties of uranyl-like ions II. Plutonyl

The electronic configuration and bonding in (PuO 2 ) 2+ are considered. The calculated energy levels can be correlated satisfactorily with the absorption spectrum of (PuO 2 ) 2+ in aqueous solution by a plausible choice of numerical parameters. The microwave resonance absorption and paramagnetic susceptibility are derived on the basis of the model, and are in good agreement with experimental results.