A semi-explicit multi-step method for solving incompressible navier-stokes equations

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predictor-corrector semi-explicit methods. In the present work, we derive a scheme based on using the fractional step technique in conjunction with explicit multi-step time integration within the framework of Galerkin-type stabilized finite element methods. We show that under certain assumptions, a Runge–Kutta scheme equipped with the fractional step leads to an efficient semi-explicit method, where the pressure Poisson equation is solved only once per time step. Thus, the computational cost of the implicit step of the scheme is minimized. The numerical example solved validates the resulting scheme and provides the insights regarding its accuracy and computational efficiency.Peer ReviewedPostprint (published version

An explicit/implicit Runge–Kutta-based PFEM model for the simulation of thermally coupled incompressible flows

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-019-00229-0A semi-explicit Lagrangian scheme for the simulation of thermally coupled incompressible flow problems is presented. The model relies on combining an explicit multi-step solver for the momentum equation with an implicit heat equation solver. Computational cost of the model is reduced via application of an efficient strategy adopted for the solution of momentum/continuity system by the authors in their previous work. The applicability of the method to solving thermo-mechanical problems is studied via various numerical examples.Peer ReviewedPostprint (author's final draft

A Unified arbitrary lagrangian-eulerian model for fluid-structure interaction problems involving flows in flexible channels

In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The model treats the fluid-solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm , one obtains the coupled problem formulated in terms of a unique kinematic variable. Resulting monolithic system is characterized by reduced variable heterogeneity resembling that of a single-media problem. The model used in conjunction with algebraic multigrid linear solver exhibits attractive convergence rates. The model is tested using a 2D and a 3D example.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors acknowledge financial support from the Ministerio de Ciencia, Innovacion e Universidades of Spain via the “Severo Ochoa” Programme for Centres of Excellence in R&D (Referece: CEX2018-000797-S) as well as via AMADEUS Project Grant (Reference: PGC2018-101655-B-I00).Peer ReviewedPostprint (published version

High heat resistance can be deceiving: dripping behavior of polyamide 4.6 in fire

Polyamide 4.6 (PA46) is a high-heat-resistant polymer, but it has no dripping resistance under fire. Three commercial grades of PA46 are investigated under UL 94 vertical fire test conditions. Their performances are discussed based on the materials' structural, thermal, and rheological properties. PA46 presents flaming drops, whereas dripping is prevented in the flame-retarded PA46. Friction-modified PA46 has increased flaming dripping. Temperature profiles of the specimens under fire and the temperature of the drops are measured by thermocouples. A UL 94 vertical test configuration consisting of two flame applications is designed to assess the quantitative dripping behavior of the set of materials by the particle finite element method (PFEM). Polymer properties (activation energy and Arrhenius coefficient of decomposition, char yield, density, effective heat of combustion, heat of decomposition, specific heat capacity, and thermal conductivity) in addition to rheological responses in high temperatures are estimated and measured as input parameters for the simulations. The dripping behavior obtained by simulated materials corresponds with the experimental results in terms of time and drop size. A consistent picture of the interplay of the different phenomena controlling dripping under fire appears to deliver a better understanding of the role of different materials’ properties.The authors thank the National Council of Technological and Scientific Development from Brazil (CNPq) for its financial support (205385/2014-1). A.T.S.D. thanks the TU Berlin for the support with a STIBET degree completion grant.Peer ReviewedPostprint (published version

Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction

We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements. The novelty of the model consists in the use of the explicit streamline integration for predicting the end-of-step configuration of the fluid domain. It is shown that this prediction considerably alleviates the time step size restrictions faced by the former Lagrangian models due to the possibility of an element inversion within one time step. The method is validated and compared with conventional approaches using three numerical examples. Time step size and corresponding Courant numbers leading to optimal behavior in terms of computational efficiency are identified.This work has been supported under the auspices of the FPDI-2013-18471 grant of the Spanish Ministerio de Economia y Competitividad as well as partially funded by the COMETAD project of the National RTD Plan (ref. MAT2014-60435-C2-1-R) of the mentioned ministry.Peer ReviewedPostprint (author's final draft

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

An explicit–implicit finite element model for the numerical solution of incompressible Navier–Stokes equations on moving grids

In this paper an efficient mesh-moving Finite Element model for the simulation of the incompressible flow problems is proposed. The model is based on a combination of the explicit multi-step scheme (Runge–Kutta) with an implicit treatment of the pressure. The pressure is decoupled from the velocity and is solved for only once per time step minimizing the computational cost of the implicit step. Novel solution algorithm alleviating time step restrictions faced by the majority of the former Lagrangian approaches is presented. The method is examined with respect to its space and time accuracy as well as the computational cost. Two numerical examples are solved: one involving a problem on a domain with fixed boundaries and the other one dealing with a free surface flow. It is shown that the method can be easily parallelized.Peer Reviewe

Improving accuracy of the moving grid particle finite element method via a scheme based on Strang splitting

Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration schemes for the resulting advective and Stokes sub-problems. For achieving efficient implementation, the pressure and the velocity in the Stokes part are decoupled via the fractional step technique as in the classical PFEM. However, at the first fractional step an explicit pressure prediction procedure for alleviating mass losses is introduced. Three test cases are solved, validating the methodology and estimating its accuracy. The numerical evidence proves that the proposed scheme improves the accuracy of the PFEM.The authors acknowledges financial support from the Ministerio de Ciencia, Innovacion y Universidades of Spain via the “Severo Ochoa” Programme for Centres of Excellence in R&D (referece: CEX2018-000797-S) as well as via AMADEUS project grant (reference: PGC2018-101655-B-I00).Peer ReviewedPostprint (author's final draft

A semi-explicit multi-step method for solving incompressible navier-stokes equations

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predictor-corrector semi-explicit methods. In the present work, we derive a scheme based on using the fractional step technique in conjunction with explicit multi-step time integration within the framework of Galerkin-type stabilized finite element methods. We show that under certain assumptions, a Runge–Kutta scheme equipped with the fractional step leads to an efficient semi-explicit method, where the pressure Poisson equation is solved only once per time step. Thus, the computational cost of the implicit step of the scheme is minimized. The numerical example solved validates the resulting scheme and provides the insights regarding its accuracy and computational efficiency.Peer Reviewe

Solution of Navier–Stokes equations on a fixed mesh using conforming enrichment of velocity and pressure

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-019-00285-6Simulation of fluid flows of multi-materials is an intriguing topic in computational mechanics. Capturing the physics of the interface between different materials poses a challenge because of the discontinuities that may occur on the interface. Several methods have been proposed in the literature to deal with this issue. In this paper, a technique based on Nitsche’s method has been employed on a fixed mesh combined with the PFEM-2 strategy for the solution of Navier–Stokes equations on multi-fluid flows. The novelty of this technique is its capability of capturing the strong and weak discontinuities and its compatibility for the application of various types of boundary conditions on the interface.The research that has been presented in this publication and the results obtained have been conducted and achieved with the support of the Ministerio de Economía y Competitividad (MINECO) from Spain and its funding program Ayudas para Contratos Predoctorales para la Formación de Doctores (ref. BES-2014-070613). Author Deniz C. Tanyildiz would like to express special thanks to the project: PARFLOW (ref. BIA2013-49007-C2-1-R). Dr. Riccardo Rossi would like to express special thanks to the project: EXAQUTE (ref. 800898). Moreover, the authors would like to express their gratitude to Dr. Joan Baiges from Polytechnical University of Catalonia, for his substantial help on Nitsche’s method.Peer ReviewedPostprint (author's final draft