An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct- quad- and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian–Lagrangian approach. This enables us to refine the computational mesh in the vicinity of the droplet parcels and accurately resolve the coupling between the two phases

Formation number of confined vortex rings

This paper investigates the formation number of vortex rings generated by a piston-cylinder mechanism in a confined tube. We use Direct Numerical Simulations (DNS) of axisymmetric confined vortex rings to study the influence of different parameters on the separation (or pinch-off) of the vortex ring from the trailing jet. It is shown that the structure of the vortex ring at pinch-off depends on the type of injection program (pulse dominated by either positive or negative acceleration ramps) and the confinement ratio D w /D , where D w is the inner diameter of the tube and D the diameter of the cylinder). For low confinement ratios ( D w /D ≤ 2), a vortex of opposite sign generated at the lateral wall strongly interacts with the vortex ring and the pinch-off is not clearly observed. The pinch-off is observed and analysed for confinement ratios D w /D ≥ 2 . 5. DNS data are used to estimate the value of the formation time, which is the time necessary for the vortex generator to inject the same amount of circulation as carried by the detached vortex ring. The confined vortex ring at pinch-off is described by the model suggested by Danaila, Kaplanski and Sazhin [A model for confined vortex rings with elliptical core vorticity distribution, Journal of Fluid Mechanics, 811 :67-94, 2017]. This model allows us to take into account the influence of the lateral wall and the elliptical shape of the vortex core. The value of the formation time is predicted using this model and the slug-flow model

Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability and Dynamics

We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently developed for nonlinear Schr{\"o}dinger equations, and we study the transverse stability of these kinks. This enables us to characterize one-dimensional planar kinks as solitonic filaments, whose stationary states and corresponding spectral stability can be characterized not only in the homogeneous case, but also in the presence of external potentials. Beyond that, the full nonlinear (transverse) dynamics of such filaments are described using the reduced, one-dimensional, adiabatic invariant formulation. For radial kinks, this approach confirms their azimuthal stability. It also predicts the possibility of creating stationary and stable ring-like kinks. In all cases we corroborate the results of our methodology with full numerics on the original sine-Gordon and $\phi^4$ models.Comment: 14 pages, 15 figure

Droplet nuclei caustic formations in exhaled vortex rings

Vortex ring (VR) structures occur in light or hoarse cough configurations. These instances consist of short impulses of exhaled air resulting to a self-contained structure that can travel large distances. The present study is the first implementation of the second order Fully Lagrangian Approach (FLA) for three-dimensional realistic flow-fields obtained by means of Computational Fluid Dynamics (CFD) and provides a method to calculate the occurrence and the intensity of caustic formations. The carrier phase flow field is resolved by means of second order accurate Direct Numerical Simulation (DNS) based on a Finite Difference approach for the momentum equations, while a spectral approach is followed for the Poisson equation using Fast Fourier Transform (FFT). The effect of the undulations of the carrier phase velocity due to large scale vortical structures and turbulence is investigated. The evaluation of the higher order derivatives needed by the second order FLA is achieved by pre-fabricated least squares second order interpolations in three dimensions. This method allows for the simulation of the clustering of droplets and droplet nuclei exhaled in ambient air in conditions akin to light cough. Given the ambiguous conditions of vortex-ring formation during cough instances, three different exhale (injection) parameters n are assumed, i.e. under-developed ([Formula: see text]), ideal ([Formula: see text]) and over-developed ([Formula: see text]) vortex rings. The formation of clusters results in the spatial variance of the airborne viral load. This un-mixing of exhumed aerosols is related to the formation of localised high viral load distributions that can be linked to super-spreading events

Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.Comment: 10 pages, 4 figure

Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R) (2004)] for the vortex distribution, a consequence of which is that the vortex distribution is strongly inhomogeneous close to the critical speed and gradually homogenizes when the rotation speed is increased. From the mathematical point of view, a novelty of our approach is that we do not use any compactness argument in the proof, but instead provide explicit estimates on the difference between the vorticity measure of the GP ground state and the minimizer of a certain renormalized energy functional.Comment: 41 pages, journal ref: Communications in Mathematical Physics: Volume 321, Issue 3 (2013), Page 817-860, DOI : 10.1007/s00220-013-1697-

Carfilzomib and dexamethasone versus bortezomib and dexamethasone for patients with relapsed or refractory multiple myeloma (ENDEAVOR): And randomised, phase 3, open-label, multicentre study

Background: Bortezomib with dexamethasone is a standard treatment option for relapsed or refractory multiple myeloma. Carfilzomib with dexamethasone has shown promising activity in patients in this disease setting. The aim of this study was to compare the combination of carfilzomib and dexamethasone with bortezomib and dexamethasone in patients with relapsed or refractory multiple myeloma. Methods: In this randomised, phase 3, open-label, multicentre study, patients with relapsed or refractory multiple myeloma who had one to three previous treatments were randomly assigned (1:1) using a blocked randomisation scheme (block size of four) to receive carfilzomib with dexamethasone (carfilzomib group) or bortezomib with dexamethasone (bortezomib group). Randomisation was stratified by previous proteasome inhibitor therapy, previous lines of treatment, International Staging System stage, and planned route of bortezomib administration if randomly assigned to bortezomib with dexamethasone. Patients received treatment until progression with carfilzomib (20 mg/m2 on days 1 and 2 of cycle 1; 56 mg/m2 thereafter; 30 min intravenous infusion) and dexamethasone (20 mg oral or intravenous infusion) or bortezomib (1·3 mg/m2; intravenous bolus or subcutaneous injection) and dexamethasone (20 mg oral or intravenous infusion). The primary endpoint was progression-free survival in the intention-to-treat population. All participants who received at least one dose of study drug were included in the safety analyses. The study is ongoing but not enrolling participants; results for the interim analysis of the primary endpoint are presented. The trial is registered at ClinicalTrials.gov, number NCT01568866. Findings: Between June 20, 2012, and June 30, 2014, 929 patients were randomly assigned (464 to the carfilzomib group; 465 to the bortezomib group). Median follow-up was 11·9 months (IQR 9·3-16·1) in the carfilzomib group and 11·1 months (8·2-14·3) in the bortezomib group. Median progression-free survival was 18·7 months (95% CI 15·6-not estimable) in the carfilzomib group versus 9·4 months (8·4-10·4) in the bortezomib group at a preplanned interim analysis (hazard ratio [HR] 0·53 [95% CI 0·44-0·65]; p<0·0001). On-study death due to adverse events occurred in 18 (4%) of 464 patients in the carfilzomib group and in 16 (3%) of 465 patients in the bortezomib group. Serious adverse events were reported in 224 (48%) of 463 patients in the carfilzomib group and in 162 (36%) of 456 patients in the bortezomib group. The most frequent grade 3 or higher adverse events were anaemia (67 [14%] of 463 patients in the carfilzomib group vs 45 [10%] of 456 patients in the bortezomib group), hypertension (41 [9%] vs 12 [3%]), thrombocytopenia (39 [8%] vs 43 [9%]), and pneumonia (32 [7%] vs 36 [8%]). Interpretation: For patients with relapsed or refractory multiple myeloma, carfilzomib with dexamethasone could be considered in cases in which bortezomib with dexamethasone is a potential treatment option. Funding: Onyx Pharmaceuticals, Inc., an Amgen subsidiary