# L. L. FerrásUniversity of Porto | UP

L. L. Ferrás

Ph.D. (Applied Mathematics)

## About

103

Publications

39,425

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823

Citations

Citations since 2017

Introduction

Center of Mathematics (CMAT), University of Minho. Resercher in Applied Mathematics (numerical solution of fractional differential equations and their application to physics and engineering; computational fluid dynamics; viscoelastic fluids).
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....................................https://luislimafr.wordpress.com/
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Education

July 2013 - August 2018

July 2008 - November 2012

September 2005 - November 2007

## Publications

Publications (103)

Viscoelastic materials are abundant in nature and present in our daily lives [...]

The focus of this work is the numerical study of stable and pulsatory flame burst in an undulating geometry, using premixed hydrogen and air (with an equivalence ratio of 1.0). This work extends other works in the literature by considering a linear temperature profile along the wall. This allows an analysis of the flow dynamics without forcing the...

In this work, we present a generalised viscoelastic model using distributed‐order derivatives. The model consists of two distributed‐order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accur...

Polymer processing techniques are of paramount importance in the manufacture of polymer parts [...]

In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. Blumen, Hierarchical analogues to fractio...

In this work, a stable and convergent numerical scheme on non-uniform time meshes is proposed, for the solution of distributed-order diffusion equations. A set of numerical results illustrates that the use of particular non-uniform time meshes provides more accurate results than the use of a uniform mesh, in the case of non-smooth solutions.Keyword...

Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method...

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations ar...

In this work we perform a numerical study on the flow around the hulls of competition kayaks with the aim of predicting accurate drag forces. The numerical simulations were first performed using the Wigley hull geometry, a typical validation case for flows around marine vessels. The total drag force and wave profiles of the hull were determined for...

Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decom...

Abstract: The impact of the optimization algorithms Adam, RMSprop, L-BFGS, and SGD with momentum on the solution of the Fractional Laplacian Equation (FLE) by physics-informed neural networks is investigated considering two different analytical solutions, one smooth and the other non-smooth. The influence of the optimization approach, the smoothnes...

Abstract: This study involves a review of existing object detection methods as well as the development of a Deep Learning model that can detect swimming pools from satellite pictures. The model was trained on a Kaggle-customized dataset and then evaluated on a newly created dataset containing aerial images. Several metrics are used to evaluate the...

Abstract: When studying complex viscoelastic fluids, the exponential form of the original Phan-Thien and Tanner (PTT) model is frequently used. A generalized version of the PTT model was recently proposed, which employs the Mittag-Leffler function to generate a new function of the trace of the stress tensor. We propose two optimization problems for...

This work presents a study of the different existing object detection algorithms and the implementation of a Deep Learning model capable of detecting swimming pools from satellite images. In order to obtain the best results for this particular task, the RetinaNet algorithm was chosen. The model was trained using a customised dataset from Kaggle and...

The exponential form of the original Phan-Thien and Tanner (PTT) model is often used to study complex viscoelastic fluids. Recently, a generalised version of the PTT model, that uses the Mittag-Leffler function to compute a new function of the trace of the stress tensor, was proposed. This new model adds one or two additional fitting parameters tha...

This work presents a numerical method for the solution of two coupled distributed-order fractional differential equations, that appear in the pure tangential flow of fluids modelled by the Distributed-Order Viscoelastic Model. We prove the solvability of the method, and, perform numerical simulations of relaxation tests.

This work presents a viscoelastic model based on distributed-order derivatives. The model generalises the fractional springpot element by considering an integral kernel that captures the continuous contribution of all elements with fractional order α ∈ (0, 1). We derive some properties of the model and perform numerical simulations considering simp...

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than th...

This work presents a detailed numerical investigation on the required development length (L=L/B) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (AR). The advent of new microfluidic technologies shifted the practical Reynolds numbers (Re) to the range of unitary (and even lower) orders of...

This work presents new semi-analytical solutions for the combined fully developed electro-osmotic pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien–Tanner model (gPTT) recently proposed by Ferrás et al. (Journal of Non-Newtonian Fluid Mechanics, 269:88–99, 2019). This generalised version of the PT...

Portuguese legislation states the compulsory reporting of the addition of amenities, such as swimming pools, to the Portuguese tax authority. The purpose is to update the property tax value, to be charged annually to the owner of each real estate.
According to MarketWatch, this decade will bring a global rise to the number of swimming pools due to...

This work combines experimental and numerical (computational fluid dynamics) data
to better understand the kinetics of the dispersion of graphite nanoplates in a polypropylene melt, using a mixing device that consists of a series of stacked rings with an equal outer diameter and alternating larger and smaller inner diameters, thereby creating a ser...

Melt mixing is a convenient method to prepare polymer nanocomposites, but the extent of the dispersion of the solid filler reached is often limited, and may compromise the anticipated performance of these materials during service. Since the efficiency of extensional flows on dispersion is now well recognized, several mixers were designed with the a...

Purpose
The purpose of this paper is to develop new boundary conditions for simulating the injection molding process of polymer melts.
Design/methodology/approach
The boundary conditions are derived and implemented to simulate real-life air vents (used to allow the air escape from the mold). The simulations are performed in the computational libr...

This Special Issue aims to gather new developments on the different areas of viscous and Viscoelastic fluid flows, ranging from mathematical modeling to experimental work. All researchers working in these areas are encouraged to submit their works. All submissions will be subject to a rapid and thorough review.
Keywords:
viscoelasticity mathemati...

In this work, we present a systematic numerical investigation of the 1:4 planar expansion creeping flow under the influence of slip boundary conditions for Newtonian and viscoelastic fluids, the latter modeled by the simplified Phan–Thien–Tanner constitutive model. The linear and nonlinear Navier slip laws were considered with the dimensionless sli...

This work presents analytical and numerical studies for pure Couette and combined Poiseuille-Couette ﬂows under slip. The ﬂuid behaviour is described by the recently proposed viscoelastic model, known as the generalised simpliﬁed Phan-Thien-Tanner constitutive equation, that considers the Mittag-Leﬄer function instead of the classical linear and ex...

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille-Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien-Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien-Tanner constitutive equation. This generalised version considers the Mittag-L...

In this work we propose a novel generalised form of the Phan-Thien and Tanner (PTT) model by considering a new functional form of the nonlinear expression characterizing the destruction of physical network junctions and entanglements. This new function of the trace of the stress tensor is given by the generalized Mittag-Leffler function, and contai...

Considering the regularity properties of the solutions of fractional diﬀerential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and non-smooth solutions of systems of fractional ordinary diﬀerential equations of the Caputo-type. We provide the error analysis of the numerical method and we il...

In this work we present a new numerical method for the solution of the distributed order time-fractional diﬀusion equation. The method is based on the approximation of the solution by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points. An error analysis...

In this work we present new numerical methods for the solution of fractional differential equations of single and distributed order that find application in the different fields of physics and engineering. We start by showing the relationship between fractional derivatives and processes like anomalous diffusion and viscoelasticity, and, we then dev...

In this work we present a hybrid numerical scheme for the solution of systems of fractional differential equations arising in several fields of engineering. The numerical scheme can deal with both smooth and non-smooth solutions, and, the idea behind the hybrid method is that of approximating the solution as a linear combination of non-polynomial f...

This work presents a simple procedure for balancing the flow in extrusion dies. The method consists in using different temperatures on the different sides of the extrusion die surface, in this way altering the local viscosity of the polymer melt, and thus the melt flow distribution. The design methodology follows a numerical trial-and-error procedu...

This work reports the developments made in improving the numerical stability of the viscoelastic solvers available in the open-source finite volume computational library \(OpenFOAM^{\textregistered }\). For this purpose, we modify the usual both-side diffusion (BSD) technique, using a new approach to discretize the explicit diffusion operator. Calc...

This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette assumption near the wall is employed, and for...

Multiphase flows are relevant in several industrial processes mainly because they are present in the production of a large diversity of products. Hence, the availability of accurate numerical modeling tools, able to cope with this type of flows, is of major significance to provide detailed information about the system characteristics, in order to g...

Fractional diﬀerential equations are becoming a hot topic in mathematics and engineering, and, in the last few decades we have witnessed a mass generalization of classical models to their fractional version. This happened due to the new properties of these fractional differential and integral operators, that take into account the memory of the proc...

In this work we discuss the connection between classical and fractional viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the fractional Maxwell model. We then develop a numerical method for the solution of two coupled fractional diﬀerential equ...

In this poster we propose a new differential viscoelastic model that takes advantage of the enhanced properties of the Mittag-Leffler function (a generalization of the exponential function).
Since the differential model is based on local operators, it reduces the computational time needed to predict the flow behavior (when compared to integral mod...

In this work we present a hybrid numerical scheme for the solution of systems of fractional differential equations arising in several fields of engineering. The numerical scheme can deal with both smooth and non-smooth solutions, and, the idea behind the hybrid method is that of approximating the solution as a linear combination of non-polynomial f...

This dissertation presents new numerical methods for the solution of fractional differential equations of single and distributed order that find application in the different fields of physics and engineering.
We start by presenting the relationship between fractional derivatives and processes like anomalous diffusion, and, we then develop new numer...

This work presents the implementation and verification of a new solver in the OpenFOAM®open source computational library. The new solver allows the numerical solution of the integral viscoelastic constitutive equations, and their coupling with the continuity and momentum equations. This solver is also more stable when compared to the previous imple...

This work presents a new design procedure for improving the flow distribution in complex profile extrusion dies. The proposed approach is based on open source software and aims to motivate both academics and industrials to consider numerical methodologies in their future developments. A new solver was implemented in OpenFOAM computational library i...

In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [A.M. Afonso, F.T. Pinho, M.A. Alves, Electro-osmosis of viscoelastic fluids and prediction of electro-elastic flow instabilities in a cross slot using a finite-volume method, Journal of Non-Newtonian Fluid Mechanics 179 (2012) 55-68] is revisited an...

This work reports the developments made to improve the numerical stability of the viscoelastic solvers available in the open-source finite-volume computational library OpenFOAM R. For this purpose we modify the usual both-side diffusion (BSD) technique using a new approach to discretize the explicit diffusion operator. Calculations performed with t...

The twin-slit rheological die can be operated in such a way that the total pressure drop is maintained constant while the shear rate in the measuring slit is changed. The device is particularly useful when coupled to an extruder and used to characterize materials that are sensitive to thermo-mechanical conditions. In the present work, the twin-slit...

This work presents a numerical study on the development length (L=L/H) required to reach fully-developed flow conditions at the entrance of a planar channel for inelastic non-Newtonian fluids modeled by the Sisko model. The simulations were carried out for low Reynolds number flows in the range 0 < Re ≤ 100, for a power law index, n, in the range 1...

On the extrusion of thermoplastic profiles, upon the forming stage that takes place in the extrusion die, the profile must be cooled in a metallic calibrator. This stage must be done at a high rate, to assure increased productivity, but avoiding the development of high temperature gradients, in order to minimize the level of induced thermal residua...

This paper reports the developments made to improve the numerical stability of the open-source finite-volume computational library OpenFOAM® developed for the numerical computation of viscoelastic fluid flows described by differential constitutive models. The improvements are based on the modification of the both-sides diffusion technique, named im...

A combined numerical and experimental approach provides an improved understanding of the correlation between flow conditions and the strength of weld lines. Weld lines form when two or more flow fronts in a fluid merge, or when the flow encounters an obstacle that forces two portions of the fluid to separate (and then rejoin at the end of the obsta...

Purpose
This work aims to provide additional insights regarding the practicability of using conventional materials in the fused filament fabrication (FFF) process.
Design/methodology/approach
Two different acrylonitryle butadiene styrene (ABS) grades are studied and compared, aiming to check to what extent the regular ABS developed for conventiona...

This work describes a theoretical and numerical investigation of viscoelastic fluid flows, considering slip boundary conditions. The viscoelastic fluid is described by the simplified
Phan-Thien-Tanner (sPTT) model, and the governing equations
with slip boundary conditions are solved by a finite volume method
using: (1) a recently proposed methodolo...

This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelasticmodels based on fractional derivatives (the Fractional MaxwellModel – FMM and the Fractional Viscoelastic Fluid – FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A thir...

In this work we present a detailed description of how to use open source based computer codes to aid the design of complex profile extrusion dies, aiming to improve its flow distribution. The work encompasses the description of the overall open-source die design methodology, the implementation of the energy conservation equation in an existing Open...

In this work we present improved design guidelines to support the die designer activity, when searching for the flow channel geometry that allows the achievement of a balanced flow distribution, in complex profile extrusion dies. The proposed methodology relies on surrogate models, obtained through a detailed and extensive numerical study, carried...

In this work we extend a numerical method developed by the group for the solution of fractional diﬀerential equations governing the ﬂow of complex ﬂuids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also...

In this work we extend a numerical method developed by the group for the solution of fractional diﬀerential equations governing the ﬂow of complex ﬂuids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also...

In this work a novel methodology to balance the flow distribution
in complex extrusion dies is proposed. For this purpose,
the profile cross section geometry is divided into simpler geometries
(L and T shaped profiles), which are balanced with a
surrogate model obtained by a detailed numerical study. The
numerical simulations are performed consider...

In this work, we present a study on numerical and experimental approaches aiming to improve our understanding about the relation between the flow conditions and the strength of weld lines in extruded profiles. For this purpose, a prototype extrusion die that comprises a movable spider leg is used to produce tapes under different flow conditions, by...

A numerical method for the solution of the coupled system of equations arising in the pure tangential annular ﬂow of fractional viscoelastic ﬂuids is presented. The method can resolve fast transients and start-up relaxations. We have distinguished two types of models, the FMM and the FVF (ideal model for ﬂuids). The results presented in this work f...

In this work we present a new numerical method for the solution of the distributed order time-fractional diffusion equation. The method is based on the approximation of the solution by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points. An error analysi...

In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye–Hückel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the...

Theoretical and Numerical Aspects of Fractional Modelling

Scope of the poster In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical tech...

In the present work the benefits of using graphics processing units (GPU) to aid the design of complex geometry profile extrusion dies, are studied. For that purpose, a 3D finite volume based code that employs unstructured meshes to solve and couple the continuity, momentum and energy conservation equations governing the fluid flow, together with a...

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation....

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction-diffusion e...

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion...

This work presents a numerical and experimental study on the flow behavior of a polymer melt around the spider leg of a prototype extrusion die, designed to study the relationship between the thermo-mechanical conditions in which the weld lines are formed and their impact. The numerical simulations will enable to study the influence of the spider l...

This work reports the implementation and verification of a new solver in OpenFOAM® open source computational library, able to cope with integral viscoelastic models based on the integral upper-convected Maxwell model. The code is verified through the comparison of its predictions with analytical solutions and numerical results obtained with the dif...

Investigation of an extrusion die designed for the production of wood-plastic-composite decking profiles shows that numerical tools help to optimize flow balance. Today, due to the continual emergence of new and sophisticated products, profile extrusion faces new challenges that are motivating the adoption of innovative design methods. The major pr...

In this work, the optimization of an extrusion die designed for the production of a wood–plastic composite (WPC) decking profile is investigated. The optimization was performed with the help of numerical tools, more precisely, by solving the continuity and momentum conservation equations that govern such flow, and aiming to balance properly the flo...

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan-Thien - Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flow under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three of the PTT variants mod...

This work investigates the steady-state slip flow of viscoelastic fluids in hydrophobic two-dimensional microchannels under the combined influence of electro-osmotic and pressure gradient forcings with symmetric or asymmetric zeta potentials at the walls. The Debye–Hückel approximation for weak potential is assumed, and the simplified Phan-Thien-Ta...

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of distributed order. Diﬀerent versions of the bioheat equation are considered, that take into account the temperature-dependent variability in the tissue perfusion, and that comprise both ﬁnite and inﬁnite speed propagation of h...