Regional deposition effects are important in the pulmonary delivery of drugs intended for the topical treatment of respiratory ailments. They also play a critical role in the systemic delivery of drugs with limited lung bioavailability. In recent years, significant improvements in the quality of pulmonary imaging have taken place, however the resolution of current imaging modalities remains inadequate for quantifying regional deposition. Computational Fluid-Particle Dynamics (CFPD) can fill this gap by providing detailed information about regional deposition in the extrathoracic and conducting airways. It is therefore not surprising that the last 15years have seen an exponential growth in the application of CFPD methods in this area. Survey of the recent literature however, reveals a wide variability in the range of modelling approaches used and in the assumptions made about important physical processes taking place during aerosol inhalation. The purpose of this work is to provide a concise critical review of the computational approaches used to date, and to present a benchmark case for validation of future studies in the upper airways. In the spirit of providing the wider community with a reference for quality assurance of CFPD studies, in vitro deposition measurements have been conducted in a human-based model of the upper airways, and several groups within MP1404 SimInhale have computed the same case using a variety of simulation and discretization approaches. Here, we report the results of this collaborative effort and provide a critical discussion of the performance of the various simulation methods. The benchmark case, in vitro deposition data and in silico results will be published online and made available to the wider community. Particle image velocimetry measurements of the flow, as well as additional numerical results from the community, will be appended to the online database as they become available in the future.

The development and assessment of an efficient parallelization method for the evaluation of reaction rates in combustion simulations is presented. Combustion simulations where the finite-rate chemistry model is employed are computationally expensive. In such simulations, a transport equation for each species in the chemical reaction mechanism has to be solved, and the resulting system of equations is typically stiff. As a result, advanced implicit methods must be applied to obtain accurate solutions using reasonable time-steps at expenses of higher computational resources than explicit or classical implicit methods.

Summary Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell‐centred velocity reconstructions, the standard first‐order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd–even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable‐density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy‐preserving scheme is applied to the momentum equations, namely, the symmetry‐preserving scheme. Furthermore, a new approach to define the far‐neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self‐igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable‐density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second‐order behaviour on unstructured meshes, and the symmetry‐preserving is reliably used in all computations. Copyright © 2016 John Wiley & Sons, Ltd.

The appearence of unphysical velocities in highly distorted meshes is a common problem in many simulations. In collocated meshes, this problem arises from the interpolation of the pressure gradient from faces to cells. Using an algebraic form for the classical incompressible Navier-Stokes equations, this problem is adressed. Starting from the work of F. X. Trias et. al. [FX.Trias et al. JCP 258: 246-267, 2014], a new approach for studying the Poisson equation obtained using the Fractional Step Method is found, such as a new interpolator is proposed in order to found a stable solution, which avoid the appearence of these unpleasant velocities. The stability provided by the interpolator is formally proved for cartesian meshes and its rotations, using fully-explicit time discretizations. The construction of the Poisson equation is supported on mimicking the symmetry properties of the differential operators and the Fractional Step Method. Then it is reinterpreted using a recursive application of the Fractional Step Method in order to study the system as an stationary iterative solver. Furthermore, a numerical analysis for unstructured mesh is also provided.

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