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In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the "space-filling" source trajectory along which the experimental data is collected. The speed of convergence is achieved by leveraging the highly isotropic nature of this trajectory to design an approximate deconvolution filter that serves as a pre-conditioner in a multi-grid scheme. We demonstrate this IR scheme for CBCT and compare convergence to that of more traditional techniques., Comment: 7 pages, 4 figures

We present a successful deployment of high-fidelity Large-Eddy Simulation (LES) technologies based on spectral/hp element methods to industrial flow problems, which are characterized by high Reynolds numbers and complex geometries. In particular, we describe the numerical methods, software development and steps that were required to perform the implicit LES of a real automotive car, namely the Elemental Rp1 model. To the best of the authors' knowledge, this simulation represents the first fifth-order accurate transient LES of an entire real car geometry. Moreover, this constitutes a key milestone towards considerably expanding the computational design envelope currently allowed in industry, where steady-state modelling remains the standard. To this end, a number of novel developments had to be made in order to overcome obstacles in mesh generation and solver technology to achieve this simulation, which we detail in this paper. The main objective is to present to the industrial and applied mathematics community, a viable pathway to translate academic developments into industrial tools, that can substantially advance the analysis and design capabilities of high-end engineering stakeholders. The novel developments and results were achieved using the academic-driven open-source framework Nektar++.

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/$hp$ element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments - in particular: the method of moving frames, which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a 'thick' strip model for the modelling of fluid-structure interaction problems in the context of vortex-induced vibrations. We conclude by commenting some directions for future code development and expansion., Comment: 21 pages, 14 figures

We examine the thermal evolution of particle number densities in the early universe when the particles have a finite diffusion length. Assuming that annihilations are impossible when the mean separation of the particles is larger than their diffusion length, we derive a version of the Boltzmann equation for freeze out in this scenario and an approximate solution, accurate to better than 2\%. The effect of a finite diffusion length is to increase the final relic freeze-out abundance over its corresponding value when diffusion effects are ignored. When diffusion is limited only by scattering off of the thermal background, and the annihilation cross section is bounded by unitarity, a significant effect on the freeze-out abundance requires a scattering cross section much larger than the annihilation cross section. A similar effect is demonstrated when the relic particles are produced via the freeze-in mechanism, but in this case the finite diffusion length is due to the scattering of particles that annihilate into the relic particle of interest. For freeze in, the effect of a finite diffusion length is to reduce the final relic particle abundance. The effects of a finite diffusion length are most important when the scattering cross section or the relic mass are very large. While we have not found a particularly compelling example where this would affect previous results, with the current interest in new dark matter candidates it could become an important consideration., Comment: 10 pages, 3 figures, discussion generalized to p-wave and higher-order annihilations, references added

We describe a semi-structured method for the generation of high-order hybrid meshes suited for the simulation of high Reynolds number flows. This is achieved through the use of highly stretched elements in the viscous boundary layers near the wall surfaces. CADfix is used to first repair any possible defects in the CAD geometry and then generate a medial object based decomposition of the domain that wraps the wall boundaries with partitions suitable for the generation of either prismatic or hexahedral elements. The latter is a novel distinctive feature of the method that permits to obtain well-shaped hexahedral meshes at corners or junctions in the boundary layer. The medial object approach allows greater control on the "thickness" of the boundary-layer mesh than is generally achievable with advancing layer techniques. CADfix subsequently generates a hybrid straight sided mesh of prismatic and hexahedral elements in the near-field region modelling the boundary layer, and tetrahedral elements in the far-field region covering the rest of the domain. The mesh in the near-field region provides a framework that facilitates the generation, via an isoparametric technique, of layers of highly stretched elements with a distribution of points in the direction normal to the wall tailored to efficiently and accurately capture the flow in the boundary layer. The final step is the generation of a high-order mesh using NekMesh, a high-order mesh generator within the Nektar++ framework. NekMesh uses the CADfix API as a geometry engine that handles all the geometrical queries to the CAD geometry required during the high-order mesh generation process. We will describe in some detail the methodology using a simple geometry, a NACA wing tip, for illustrative purposes. Finally, we will present two examples of application to reasonably complex geometries proposed by NASA as CFD validation cases., Comment: Pre-print accepted to the 2018 AIAA Aerospace Sciences Meeting

A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the initial mesh are manipulated using metric tensors to obtain target elements. The nonlinear optimisation in turns adapts the final high-order mesh to best fit the description of the target elements by minimising the element distortion. Encouraging preliminary results prove that the method behaves well and can be used in the future for more extensive work which shall include the use of error indicators from CFD simulations., Comment: Pre-print accepted to the 26th International Meshing Roundtable

Sasankan et al, have recently claimed that there are significant deviations in the phase-space distributions of the kinetic energies of nuclei from the Maxwell-Boltzmann form usually assumed in BBN, and further, that these deviations lead to big changes in the predicted light-element abundances. Solving the relativistic Boltzmann equation perturbatively, we explicitly show that these deviations are not 20% as claimed, but rather are about 10^-17 in size and hence cannot significantly alter the predicted light-element abundances. We discuss and compute two related effects: O(0.1%) corrections to the kinetic distributions of nuclei that arise from small relativistic corrections to the MB distribution and a much smaller effect, nuclear kinetic drag, which arises from the heat transferred from the EM plasma to nuclei that is needed to maintain kinetic equilibrium., Comment: 10 pages, extended comparison to Sasankan et al

The hypothetical $SU(3)$ flavor-singlet dibaryon state $S$ with strangeness $-2$ has been discussed as a dark-matter candidate capable of explaining the curious 5-to-1 ratio of the mass density of dark matter to that of baryons. We study the early-universe production of dibaryons and find that irrespective of the hadron abundances produced by the QCD quark/hadron transition, rapid particle reactions thermalized the $S$ abundance, and it tracked equilibrium until it "froze out" at a tiny value. For the plausible range of dibaryon masses (1860 - 1890 MeV) and generous assumptions about its interaction cross sections, $S$'s account for at most $10^{-11}$ of the baryon number, and thus cannot be the dark matter. Although it is not the dark matter, if the $S$ exists it might be an interesting relic., Comment: 11 pages, 5 figures