A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily implement various numerical algorithms.Two robust and optimised numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models

The super thin external pudendal artery (STEPA) free flap for oropharyngeal reconstruction – A case report

The radial forearm flap is one of the most used micro‐anastomotic flaps in cervicofacial reconstruction in a carcinological context. This flap is an ideal in terms of reliability and fineness; it has, however, some disadvantages in terms of the functional and aesthetic complications of its donor site. In alternative to a radial forearm free flap, we report the use of the free super thin external pudendal artery flap (STEPA flap) for an oropharyngeal reconstruction. The aim was to decrease the donor site morbidity. A 71‐years‐old man with a T2N0M0 oropharyngeal squamous cell carcinoma has undergone surgical treatment. A left STEPA free flap was performed to reconstruct a defect about 8 × 6 cm2. This flap was designed as a half‐scrotal free flap sized 9 × 7 cm2 and was inset after tunneling of the pedicle at the floor of the mouth. A surgical revision was needed on the 15th day postoperative for disunion. There was no skin flap failure. After 12 month of follow‐up, no complication was observed at the donor site and no erectile dysfunction was recorded. Its characteristics in terms of fineness, flexibility, ease of conformation, and pedicle length are similar to those of the radial forearm flap with less aesthetic and functional sequelae of the donor site. The STEPA flap may be a promising free flap in oropharyngeal or oral cavity reconstruction

Risk Factors for Pharyngocutaneous Fistula After Total Pharyngolaryngectomy

Purpose:To evaluate the risk factors of pharyngocutaneous fistula after total pharyngolaryngectomy (TPL) in orderto reduce theirincidence and propose a perioperative rehabilitation protocol.Materials and Methods:This was a multicenter retrospectivestudy based on 456 patients operated for squamous cell carcinoma by total laryngectomy or TPL. Sociodemographic, medical,surgical, carcinologic, and biological risk factors were studied. Reactive C protein was evaluated on post-op day 5. Patients weredivided into a learning population and a validation population with patients who underwent surgery between 2006 and 2013 andbetween 2014 and 2016, respectively. A risk score of occurrence of salivary fistula was developed from the learning population dataand then applied on the validation population (temporal validation).Objective:To use a preoperative risk score in order tomodify practices and reduce the incidence of pharyngocutaneous fistula.Results:Four hundred fifty-six patients were included,328 in the learning population and 128 in the validation population. The combination of active smoking over 20 pack-years, ahistory of cervical radiotherapy, mucosal closure in separate stitches instead of running sutures, and the placement of a pedicleflap instead of a free flap led to a maximum risk of post-op pharyngocutaneous fistula after TPL. The risk score was discriminantwith an area under the receiver operating characteristic curve of 0.66 (95% confidence interval [CI]¼0.59-0.73) and 0.70 (95% CI¼0.60-0.81) for the learning population and the validation population, respectively.Conclusion:A preoperative risk score couldbe used to reduce the rate of pharyngocutaneous fistula after TPL by removing 1 or more of the 4 identified risk factors

Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates

Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux de Bose. Depuis lors, de nombreux physiciens,mathématiciens et numériciens se sont intéressés au condensat de Bose-Einstein et à son caractère superfluide. Nous proposons dans cette étude des méthodes numériques ainsi qu’un code informatique pour la simulation d’un condensat de Bose-Einstein en rotation. Le principal modèle mathématique décrivant ce phénomène physique est une équation de Schrödinger présentant une non-linéarité cubique,découverte en 1961 : l’équation de Gross-Pitaevskii (GP). En nous appuyant sur le logiciel FreeFem++,nous nous servons d’une discrétisation spatiale en éléments-finis pour résoudre numériquement cette équation. Une méthode d’adaptation du maillage à la solution et l’utilisation d’éléments-finis d’ordre deux nous permet de résoudre finement le problème et d’explorer des configurations complexes en deux ou trois dimensions d’espace. Pour sa version stationnaire, nous avons développé une méthode de gradient de Sobolev ou une méthode de point intérieur implémentée dans la librairie Ipopt. Pour sa version instationnaire, nous utilisons une méthode de Time-Splitting combinée à un schéma de Crank-Nicolson ou une méthode de relaxation. Afin d’étudier la stabilité dynamique et thermodynamique d’un état stationnaire, le modèle de Bogoliubov-de Gennes propose une linéarisation de l’équation de Gross-Pitaevskii autour de cet état. Nous avons élaboré une méthode permettant de résoudre ce système aux valeurs et vecteurs propres, basée sur un algorithme de Newton ainsi que sur la méthode d’Arnoldi implémentée dans la librairie Arpack.The phenomenon of condensation of a boson gas when cooled to zero degrees Kelvin was described by Einstein in 1925 based on work by Bose. Since then, many physicists, mathematicians and digitizers have been interested in the Bose-Einstein condensate and its superfluidity. We propose in this study numerical methods as well as a computer code for the simulation of a rotating Bose-Einstein condensate.The main mathematical model describing this phenomenon is a Schrödinger equation with a cubic nonlinearity, discovered in 1961: the Gross-Pitaevskii (GP) equation. By using the software FreeFem++ and a finite elements spatial discretization we solve this equation numerically. The mesh adaptation to the solution and the use of finite elements of order two allow us to solve the problem finely and to explore complex configurations in two or three dimensions of space. For its stationary version, we have developed a Sobolev gradient method or an internal point method implemented in the Ipopt library. .For its unsteady version, we use a Time-Splitting method combined with a Crank-Nicolson scheme ora relaxation method. In order to study the dynamic and thermodynamic stability of a stationary state,the Bogoliubov-de Gennes model proposes a linearization of the Gross-Pitaevskii equation around this state. We have developed a method to solve this eigenvalues and eigenvector system, based on a Newton algorithm as well as the Arnoldi method implemented in the Arpack library

Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein

The phenomenon of condensation of a boson gas when cooled to zero degrees Kelvin was described by Einstein in 1925 based on work by Bose. Since then, many physicists, mathematicians and digitizers have been interested in the Bose-Einstein condensate and its superfluidity. We propose in this study numerical methods as well as a computer code for the simulation of a rotating Bose-Einstein condensate.The main mathematical model describing this phenomenon is a Schrödinger equation with a cubic nonlinearity, discovered in 1961: the Gross-Pitaevskii (GP) equation. By using the software FreeFem++ and a finite elements spatial discretization we solve this equation numerically. The mesh adaptation to the solution and the use of finite elements of order two allow us to solve the problem finely and to explore complex configurations in two or three dimensions of space. For its stationary version, we have developed a Sobolev gradient method or an internal point method implemented in the Ipopt library. .For its unsteady version, we use a Time-Splitting method combined with a Crank-Nicolson scheme ora relaxation method. In order to study the dynamic and thermodynamic stability of a stationary state,the Bogoliubov-de Gennes model proposes a linearization of the Gross-Pitaevskii equation around this state. We have developed a method to solve this eigenvalues and eigenvector system, based on a Newton algorithm as well as the Arnoldi method implemented in the Arpack library.Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux de Bose. Depuis lors, de nombreux physiciens,mathématiciens et numériciens se sont intéressés au condensat de Bose-Einstein et à son caractère superfluide. Nous proposons dans cette étude des méthodes numériques ainsi qu’un code informatique pour la simulation d’un condensat de Bose-Einstein en rotation. Le principal modèle mathématique décrivant ce phénomène physique est une équation de Schrödinger présentant une non-linéarité cubique,découverte en 1961 : l’équation de Gross-Pitaevskii (GP). En nous appuyant sur le logiciel FreeFem++,nous nous servons d’une discrétisation spatiale en éléments-finis pour résoudre numériquement cette équation. Une méthode d’adaptation du maillage à la solution et l’utilisation d’éléments-finis d’ordre deux nous permet de résoudre finement le problème et d’explorer des configurations complexes en deux ou trois dimensions d’espace. Pour sa version stationnaire, nous avons développé une méthode de gradient de Sobolev ou une méthode de point intérieur implémentée dans la librairie Ipopt. Pour sa version instationnaire, nous utilisons une méthode de Time-Splitting combinée à un schéma de Crank-Nicolson ou une méthode de relaxation. Afin d’étudier la stabilité dynamique et thermodynamique d’un état stationnaire, le modèle de Bogoliubov-de Gennes propose une linéarisation de l’équation de Gross-Pitaevskii autour de cet état. Nous avons élaboré une méthode permettant de résoudre ce système aux valeurs et vecteurs propres, basée sur un algorithme de Newton ainsi que sur la méthode d’Arnoldi implémentée dans la librairie Arpack

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily implement various numerical algorithms.Two robust and optimised numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models

A finite-element toolbox for the stationary Gross–Pitaevskii equation with rotation

International audienc

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily implement various numerical algorithms.Two robust and optimised numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models

A finite-element toolbox for the stationary Gross–Pitaevskii equation with rotation

International audienc

Assessment of Fan/Airframe aerodynamic performance using 360° uRANS computations: Code-to-Code comparison between ONERA, DLR, NLR and Airbus

International audienceIn todays context of increased focus on fuel efficiency and environmental impact, turbofan engine developments continue towards ever increasing bypass ratio engine designs, with so-called Ultra-High Bypass Ratio (UHBR) engines becoming an interesting option as a potential powerplant for future commercial transport aircraft. These engines promise low specific fuel consumption at the engine level, but the resulting size of the nacelles pose challenges in terms of the installation on the airframe. Thus their integration on an aircraft requires careful consideration of complex engine-airframe interactions impacting performance, aeroelastics and aeroacoustics both on the airframe and the engine sides.As a partner in the EU funded Clean Sky 2 project ASPIRE, ONERA, DLR and NLR are contributing with Airbus to an investigation of numerical analysis approaches, which draws on a generic representative UHBR engine configuration specifically designed in the frame of the project. In the present paper, a code-to-code comparison of 360° uRANS computations, including an isolated nacelle with a geometrically fully modeled fan and OGV (Outlet Guide Vane) stage, is proposed. This code-to-code comparison is done between the structured solver of the elsA code (structured and unstructured ONERA-Airbus-Safran code, developed by ONERA), the ENFLOW solver (structured, developed by NLR), the TRACE solver (structured, developed by DLR), the TAU solver (unstructured, developed by DLR). Results are presented in terms of global values (Mass-flows, Fan Pressure and Temperature Ratio, efficiencies) and local flow distributions