On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single‐point data. Alternatively, relative pressure fields can be reconstructed from imaging‐based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher‐order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second‐order differentiation without requiring surface integrals. In‐silico and in‐vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection‐related errors

Práticas de produção mais limpa num fabricante de eletrodomésticos do setor de linha branca: um estudo de caso

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-graduação em Engenharia de Produção, Florianópolis, 2013A Produção mais Limpa tem ganhado significativa atenção das Empresas de Manufatura como uma estratégia pró-ativa em relação à gestão de meio ambiente, possibilitando a geração de benefícios tanto ambientais como econômicos. No entanto, ainda são escassas as publicações no setor que desempenha um papel importante no cenário econômico nacional, o Setor de Eletrodomésticos de Linha Branca. Nesse contexto, o presente trabalho objetiva analisar as principais práticas de Produção Mais Limpa (P+L) nos processos produtivos de um fabricante do setor de eletrodomésticos de linha branca, mais especificamente no desenvolvimento de novos processos de fabricação de refrigeradores e na gestão dos processos fabris atuais. Por meio da aplicação de uma survey de avaliação do nível de absorção da produção mais limpa na empresa estudada, observou-se que a empresa em questão apresenta um engajamento significativo com a P+L, entretanto, há grandes oportunidade de implantação de projetos de P+L com a redução de barreiras organizacionais que dificultam a realização de novas implementações. Através da criação de um protocolo de identificação de práticas de Produção mais Limpa e da análise detalhada destas, o trabalho consolidou uma lista de práticas que pode ser uma referência para o setor, tais como a substituição de antigas linhas de pintura, o reaproveitamento da água de estação de tratamento de efluentes, a mudança no tratamento de chapas metálicas, entre outros. Com enfoque na melhoria do nível de implementação da Produção mais Limpa na empresa em questão, uma lista de barreiras foi capturada e comparada com a literatura existente, servindo de referência para o setor e para trabalhos futuros. Por fim, como recomendação de futuros estudos, sugere-se a Avaliação do Nível de Absorção da Produção mais Limpa em outras organizações do mesmo setor, possibilitando o estabalecimento de um panorama da P+L na industria nacional de Eletrodomésticos de Linha Branca. Abstract: The Cleaner Production has gained significant attention of Manufacturing Enterprises as a proactive strategy for the management of the environment, allowing the generation of both environmental and economic benefits. However, there are insufficient publications in the sector that plays an important role in national economic scenario, the Sector of Household Appliances. In this context, this paper aims to analyze the main practices of Cleaner Production (CP) in the production processes of a manufacturer in the industry of white goods, more specifically in the development of new manufacturing processes and management of current manufacturing processes of refrigerators. Through the application of a survey to assess the level of uptake of cleaner production in the company studied, it was observed that the company in question has a meaningful engagement with the CP, however, there is great opportunity to implement Cleaner Production projects with the reduction of organizational barriers that hinder the realization of new implementations. By creating a protocol for identifying cleaner production practices and detailed analysis of these, this work has consolidated a list of practices that can be a reference for the sector, such as the replacement of old paint lines, the water reuse treatment plant effluent, the change in the treatment of metal plates, among others. With a focus on improving the level of implementation of Cleaner Production in the company in question, a list of barriers was captured and compared with the existing literature, serving as a reference for the sector and for future work. Finally, as a recommendation for future studies, we suggest the evaluation of Cleaner Production uptake in other organizations in the same sector, allowing to obtain an overview of the CP in the National Industry of Household Appliances

Implicit-explicit schemes for incompressible flow problems with variable viscosity

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of the diffusive term explicitly to reduce the coupling between the velocity components. We present different, both monolithic and fractional-step, IMEX alternatives for the variable-viscosity Navier--Stokes system, analysing their theoretical and algorithmic properties. Stability results are proven for all the methods presented, with all these results being unconditional, except for one of the discretisations using a fractional-step scheme, where a CFL condition (in terms of the problem data) is required for showing stability. Our analysis is supported by a series of numerical experiments

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest

Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow

[EN] In numerous engineering applications, such as polymer or blood flow, the dependence of fluid viscosity on the local shear rate plays an important role. Standard techniques using inf-sup stable finite elements lead to saddle-point systems posing a challenge even for state-ofthe-art solvers and preconditioners. Alternatively, projection schemes or time-splitting methods decouple equations for velocity and pressure, resulting in easier to solve linear systems. Although pressure and velocity correction schemes of high-order accuracy are available for Newtonian fluids, the extension to generalised Newtonian fluids is not a trivial task. Herein, we present a split-step scheme based on an explicit-implicit treatment of pressure, viscosity and convection terms, combined with a pressure Poisson equation with fully consistent boundary conditions. Then, using standard equal-order finite elements becomes possible. Stability, flexibility and efficiency of the splitting scheme is showcased in two challenging applications involving aortic aneurysm flow and human phonation.The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.Schussnig, R.; Pacheco, D.; Kaltenbacher, M.; Fries, T. (2022). Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 335-344. https://doi.org/10.4995/YIC2021.2021.12217OCS33534

An efficient split-step framework for non-Newtonian incompressible flow problems with consistent pressure boundary conditions

Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids, since the additional terms due to the non-zero viscosity gradient couple all velocity components again. Moreover, classical pressure correction methods are not consistent with the non-Newtonian setting, which can cause numerical artifacts such as spurious pressure boundary layers. Although consistent reformulations have been recently developed, the additional projection steps needed for the viscous stress tensor incur considerable computational overhead. In this work, we present a new time-splitting framework that handles such important issues, leading to an efficient and accurate numerical tool. Two key factors for achieving this are an appropriate explicit–implicit treatment of the viscous and convective nonlinearities, as well as the derivation of a pressure Poisson problem with fully consistent boundary conditions and finite-element-suitable regularity requirements. We present first- and higher-order stepping schemes tailored for this purpose, as well as various numerical examples showcasing the stability, accuracy and efficiency of the proposed framework

Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters

An Equal-Order Finite Element Framework for Incompressible Non-Newtonian Flow Problems

Various materials of engineering and biomedical interest can be modelled as generalised Newtonian fluids, i.e., via an apparent viscosity depending locally on the flow field. In spite of the particular features of those models, they are often handled in practice by classical numerical techniques originally conceived for Newtonian fluids. Methods designed specifically for the generalised case are rather scarce in the literature, as well as their use in practical applications. As it turns out, tackling nonNewtonian problems with standard finite element formulations can have undesired consequences such as the induction of spurious pressure boundary layers and the emergence of natural boundary conditions not suitable for realistic flow scenarios. In this context, we introduce a novel framework that deals with those issues while maintaining simplicity and low computational cost. The new stabilised formulation is based on a modified system combining the continuity equation with a Poisson equation for the pressure and consistent pressure boundary conditions. A weak enforcement of the rheological law is employed to enable full consistency even for first-order finite element pairs. Simple numerical examples are provided to demonstrate the potential of our method in yielding accurate solutions for relevant problems

A global residual‐based stabilization for equal‐order finite element approximations of incompressible flows

Due to simplicity in implementation and data structure, elements with equal-order interpolation of velocity and pressure are very popular in finite-element-based flow simulations. Although such pairs are inf-sup unstable, various stabilization techniques exist to circumvent that and yield accurate approximations. The most popular one is the pressure-stabilized Petrov–Galerkin (PSPG) method, which consists of relaxing the incompressibility constraint with a weighted residual of the momentum equation. Yet, PSPG can perform poorly for low-order elements in diffusion-dominated flows, since first-order polynomial spaces are unable to approximate the second-order derivatives required for evaluating the viscous part of the stabilization term. Alternative techniques normally require additional projections or unconventional data structures. In this context, we present a novel technique that rewrites the second-order viscous term as a first-order boundary term, thereby allowing the complete computation of the residual even for lowest-order elements. Our method has a similar structure to standard residual-based formulations, but the stabilization term is computed globally instead of only in element interiors. This results in a scheme that does not relax incompressibility, thereby leading to improved approximations. The new method is simple to implement and accurate for a wide range of stabilization parameters, which is confirmed by various numerical examples