An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries

We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal fluid-plasma model on adaptive Cartesian grids, extended to also account for charging of insulating surfaces. We discuss the spatial and temporal discretization methods, and show that the resulting overall method is second order convergent, monotone, and conservative (for smooth solutions). Weak scalability with parallel efficiencies over 70\% are demonstrated up to 8192 cores and more than one billion cells. We then demonstrate the use of adaptive mesh refinement in multiple two- and three-dimensional simulation examples at modest cores counts. The examples include two-dimensional simulations of surface streamers along insulators with surface roughness; fully three-dimensional simulations of filaments in experimentally realizable pin-plane geometries, and three-dimensional simulations of positive plasma discharges in multi-material complex geometries. The largest computational example uses up to $800$ million mesh cells with billions of unknowns on $4096$ computing cores. Our use of computer-aided design (CAD) and constructive solid geometry (CSG) combined with capabilities for parallel computing offers possibilities for performing three-dimensional transient plasma-fluid simulations, also in multi-material complex geometries at moderate pressures and comparatively large scale.Comment: 40 pages, 21 figure

Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA

Implicit Large-Eddy Simulations of Hot and Cold Supersonic Jets in Loci-CHEM

This paper introduces a 4th-order accurate low-dissipation flux scheme for use on un- structured CFD codes, and compares this flux scheme with two others for LES calculations of hot and cold supersonic jets. The flux schemes are compared with experimental profiles of jet centerline Mach number, total temperature and total pressure, with jet spreading rate data, and with near- field acoustic measurements. The influence of grid resolution on these solution accuracy is also evaluated. The new low-dissipation flux scheme is shown to be stable on a high-speed compressible turbulent ow problem, and to be significantly more accurate than the existing baseline flux approach

A robust immersed boundary method for flow in complex geometries: study of aerosol deposition in the human extrathoracic airways

The flow and the transport of particles in the human respiratory system dictate the effectiveness of therapeutic aerosols used in inhaled drug delivery. The aerosol particles are generally inhaled through the mouth, passing by the throat before reaching the targeted areas in the lungs. Therefore, knowledge of the particle deposition in the mouth-throat region is critical in the design of effective inhalation devices for optimum delivery to the lungs. Numerical simulations offer a non-invasive and cost-effective alternative to in vivo and in vitro tests. However, accurate prediction remains a challenge for numerical models due to the complexity of the flow in the extrathoracic airways. A robust immersed boundary method for flow in complex geometries is proposed. This greatly simplifies the task of grid generation and eliminates the problems associated with grid quality that exist for boundary-fitted grid techniques. The proposed method is an extension to the momentum forcing approach onto curvilinear coordinates and applies an iterative procedure to compute the forcing term implicitly, which stabilizes the scheme for higher Reynolds numbers. The use of a curvilinear grid minimizes the number of unused cells outside the geometry and increases the efficiency of the numerical scheme. The method is validated against numerical and experimental data in the literature for a number of test cases on both Cartesian and curvilinear grids. The results show good agreement with previous studies. Direct numerical simulations were performed in a number of realistic mouth and throat geometries obtained from MRI scans. A Lagrangian particle tracking scheme was employed to advance the particles dynamically, and total and regional deposition efficiencies were determined and compared to in vitro data. The effect of inflow turbulence and intersubject variation on deposition was studied. Geometric variation has a large impact on total deposition whereas the effect of inflow turbulence is confined to oral deposition

Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations

Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far systematic code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH's gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH's performance is much better for supersonic turbulence. [Abridged]Comment: 22 pages, 20 figures, accepted in MNRAS. Includes a rebuttal to arXiv:1111.1255 of D. Price and significant revisions to address referee comments. Conclusions of original submission unchange

Multifluid Eulerian modeling of dense gas–solids fluidized bed hydrodynamics: Influence of the dissipation parameters

Computational fluid dynamic (CFD) models must be thoroughly validated before they can be used with confidence for designing fluidized bed reactors. In this study, validation data were collected from a fluidized bed of (Geldart's group B) alumina particles operated at different gas velocities involving two fluidization hydrodynamic regimes (bubbling and slugging). The bed expansion, height of bed fluctuations and frequency of fluctuations were measured from videos of the fluidized bed. The Eulerian–Eulerian two fluid model MFIX was used to simulate the experiments. Two different models for the particle stresses—Schaeffer [Syamlal, M., Rogers, W., O’Brien, T.J., 1993. MFIX documentation: theory guide. Technical Report DOE/METC-94/1004 (DE9400087), Morgantown Energy Technology Centre, Morgantown, West Virginia (can be downloaded from Multiphase Flow with Interphase eXchanges (MFIX) website left angle brackethttp://www.mfix.orgright-pointing angle bracket); Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66, 61–74.] and Princeton [Srivastava, A., Sundaresan, S., 2003. Analysis of a frictional–kinetic model for gas–particle flow. Powder Technology 129(1–3), 72–85.] models—and different values of the restitution coefficient and internal angle of friction were evaluated. 3-D simulations are required for getting quantitative and qualitative agreement with experimental data. The results from the Princeton model are in better agreement with data than that from the Schaeffer model. Both free slip and Johnson–Jackson boundary conditions give nearly identical results. An increase in coefficient of restitution (e) from 0.8 to 1 leads to larger bed expansions and lower heights of fluctuations in the bubbling regime, whereas it leads to unchanged bed expansion and to a massive reduction in the height of fluctuations in the slugging regime. The angle of internal friction (φ) in the range 10–40ring operator does not affect the bed expansion, but its reduction significantly reduces the height of fluctuations

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks