Simulación del comportamiento de materiales viscoelásticos y aplicación a la identificación de las propiedades mecánicas de la pared arterial

La simulación del comportamiento mecánico es una herramienta de gran importancia en las Ingenierías Civil y Mecánica. De igual forma, en la práctica médica es primordial la evaluación de las propiedades el asticas y viscosas de los tejidos biológicos debido a que estas pueden evidenciar un mal funcionamiento de la pared arterial. Por esta razón, en esta tesis, se desarrollan códigos para la simulación del comportamiento viscoel astico, y se evalúa su aplicabilidad en la identificación de las propiedades mecánicas de la pared arterial a partir de medidas experimentales in-vitro de presión y diámetro arterial. Se conoce que la pared arterial esta conformada por distintos materiales anisótropos, presentando cada uno diferentes respuestas reológicas. Sin embargo, el diagnóstico médico es usualmente realizado a partir de un conjunto de parámetros que caracterizan el comportamiento global de la pared arterial. Por lo anterior, en esta tesis, se desarrolla un código tridimensional viscoelástico e isótropo que permite considerar las grandes deformaciones. Más aún, para la identificación se considera un modelo de pared arterial perfectamente cilíndrica, compuesta por un unico material viscoelástico estándar, que permite considerar una pared arterial gruesa. Los códigos son validados utilizando soluciones analíticas y resultados numéricos obtenidos por otros códigos. Los códigos son utilizados para la identificación de propiedades en siete arterias de ovejas. Para la comparación con la bibliografía se desarrollan otros dos códigos que asumen la hipótesis de pequeñas deformaciones. También se utilizan los códigos que admiten las grandes deformaciones para la identificación, logrando cuantificar el efecto de la hipótesis de pequeñas deformaciones en el valor de los parámetros obtenidos. Se concluye que los resultados de los códigos de pequeñas deformaciones son comparables a los de la bibliografía, mientras que los del código de grandes deformaciones presentan diferencias significativas.The simulation of the mechanical behavior is a highly important tool for Civil and Mechanical Engineering. Likewise, in medical practice, evaluating parameters such as elastic and viscose properties of biological tissues is fundamental since they can show a malfunction on the arterial wall. Taking these into consideration, in this thesis, codes are developed in order to simulate the viscoelastic behavior, and to evaluate the applicability in the identification of the mechanical properties of the arterial wall considering experimental measures of arterial pressure and diameter. It is known that the arterial wall is formed by distinct anisotropic materials with diferent rheological responses. However, the current medical diagnosis is based on a set of parameters which characterize the arterial wall from a global point of view. For that reason, in this work a tridimensional viscoelastic and isotropic code is developed, which allows an analysis under large deformations. Moreover, a simple model is considered for the identification where the artery is perfectly cylindrical and constituted by a unique standard viscoelastic material, which allows considering a thick arterial wall. The codes are validated using analytical solutions and numerical results obtained with other codes. The codes are used for identifying properties of seven sheep arteries. In order to compare with the bibliography, other two codes for small deformation analysis are developed. The large deformation codes are also used for the identifi2cation of the mechanical properties in order to quantify the efect of the small deformation hypothesis on the values obtained for the parameters. It is concluded that the results of the small deformations codes are comparable with those of the bibliography, while the results of the large deformations codes present notorious diferences

Analysis of high-order interpolation schemes for solving linear problems in unstructured meshes using the finite volume method

Finite-volume strategies in fluid-structure interaction problems would be of crucialvimportance in many engineering applications such as in the analysis of reed valves in reciprocating compressors. The efficient implementation of this strategy passes from the formulation of reliable high-order schemes on 3D unstructured meshes. The development of high-order models is essential in bending-dominant problems, where the phenomenon of shear blocking appears. In order to solve this problem, it is possible to either increase the number of elements or increase the interpolation order of the main variable. Increasing the number of elements does not always yield good results and implies a very high computational cost that, in real problems, is inadmissible. Using unstructured meshes is also vital because they are necessary for real problems where the geometries are complex and depart from canonical rectangular or regular shapes. This work presents a series of tests to demonstrate the feasibility of a high-order model using finite volumes for linear elasticity on unstructured and structured meshes. The high-order interpolation will be performed using two different schemes such as the Moving Least Squares (MLS) and the Local Regression Estimators (LRE). The reliability of the method for solving 2D and 3D problems will be verified by solving some known test cases with an analytical solution such as a thin beam or problems where stress concentrations appear.P. Castrillo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC (109 FPI-UPC 2018). The authors are supported by the Ministerio de Economía y Competitividad, Spain, RETOtwin project (PDC2021-120970-I00).Peer ReviewedPostprint (published version

Reed valve simulation using 3D high-order finite volume and finite element methods

The shear locking effect occurs in bending-dominant computational solid dynamics problems due to the inability of the element edges to bend, causing the appearance of artificial shear deformation. A common real example where this effect appears is in compressor reed valves. The problem can be solved by using very refined meshes or by employing high-order discretization models. This is straightforward in FEM but not fully mature for FVM models. In this work, a reed valve problem with impact is solved by means of the high-order FVM structural dynamic solver previously presented by the authors. A new strategy to deal with the impact between the valve and the solid seat is presented. Results are verified by comparison to a past experimental work and compared to those obtained by a structural FEM solver, demonstrating the reliability of this new FVM-CSD methodology.P. Castrillo gratefully acknowledges the Universitat Politecnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC (109 FPI-UPC 2018).Postprint (published version

Simulation of fluid-structure interaction and impact force on a reed valve

The cyclic impact force between a reed valve and the seat plate is the main reason of the valve failure in many thermo-technical devices as compressors, engines, etc. According to experimental observations the latter is due to fatigue and usually occurs in the leading part of the valve ‘neck’. In this work, a complex numerical analysis is presented aimed to studying the external forces and internal stresses suffered by the valve. In particular, the impact force between the valve and the seat is studied. The numerical analysis relies on the coupled synergy of two different simulation concepts. In order to do so, two codes are used: (1) first, the in-house Computational Fluid Dynamics (CFD) code presented in [1] is employed to simulate the Fluid-Structure Interaction (FSI) between gas and valve, extracting reference data for valve displacement and external gas pressures; (2) second, the analysis of the internal structure stresses, together with the impact forces with the plate is implemented in a Computational Solid Dynamics (CSD) code developed in FreeFEM++ [2]. The impact force representation is based on the formulation presented in [3] where a conserving algorithm for frictionless dynamic contact/impact is developed. Due to the importance of obtaining an adequate impact force, an exhaustive study is carried out on its characterization in terms of numerical parameters, such as the penalty stiffness. Under this framework, the valve displacement and impact velocities are verified. Hence, impact forces are analysed in different scenarios, obtaining interesting observations about stresses distribution, with a particular focus on the points where failure is experienced.The authors acknowledge Voestalpine Precision Strip AB company for the previous research collaboration project that allowed to validate experimentally the presented numerical methods. P. Castrillo gratefully acknowledges the Universitat Politecnica de Catalunya and Banco Santander for the financial ` support of his predoctoral grant FPI-UPC (109 FPI-UPC 2018). E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060). This work has also been financially supported by a competitive R+D project (ENE2017-88697-R) by the Spanish Research Agency.Postprint (published version

High-order finite volume method for solid dynamics in fluid-structure interaction applications

A la portada: "Centre Tecnològic de Transferència de Calor"(English) This thesis aims at developing a high-order finite volume method for solid dynamics on unstructured three-dimensional meshes. The adoption of high-order interpolation methods has a key importance in the efficient application of numerical methods for the resolution of real engineering problems where stress concentration occurs, and it helps to avoid the appearance of the well-known shear locking effect. Avoiding such a detrimental effect would be possible without adopting high-order schemes but with more costly and complex numerical simulations. This thesis has been developed within the Heat and Mass Transfer Technological Center research group, where structural analysis through numerical methods is a developing field of research. Besides, until now, there has been no development of the finite volume method with high-order interpolation on unstructured meshes. Hence, this thesis is the first attempt to develop this kind of methodology in the general field of study of computational solid mechanics. This work is developed into five chapters. The introduction presents a review of the bibliography, motivations, and objectives. The following three chapters reveal, through different examples, the validation and verification of the proposed mathematical formulation. It is worth noting that much of the content included in these three chapters has already been presented or published in international journals and conferences. However, some changes have been introduced with respect to the original documents. For instance, many validations and verification examples were created specifically for this thesis. The last chapter summarizes the main contributions and proposes ideas to expand this thesis in the future. In detail, this work starts by introducing the historical development of the finite volume method to solve solid problems, presenting an example where the shear locking phenomenon appears and may affect the solution of bending-dominant real problems. Next, the mathematical formulation is displayed with all the theoretical concepts needed to reproduce the method, from basic concepts of solid mechanics to the introduction of the two adopted interpolation methods: moving least squares and local regression estimators. In addition, the used spatial and temporal discretization are presented, as well as the resolution process through the Newton-Raphson method, and the nonlinear problems associated with geometric or material nonlinearities. Following the above, the verification and validation of the presented method are carried out. An exhaustive analysis of all the parameters involved in formulating both two-dimensional and three-dimensional problems is performed. Likewise, in all the examples, the results are compared with analytical solutions and with solutions obtained by other methods. Subsequently, the analysis of an industrial example carried out in collaboration with the Voestalpine company is presented. The objective of this collaboration was to characterize the behavior of the reed valve of a compressor in its cyclic operation. The company developed a custom-built impact fatigue test rig, from which displacement measurements were obtained and used to validate the method. The experiment measures the displacement of the valve as the compressed air opens and closes it by repeatedly hitting the seat, which leads to valve failure due to fatigue stresses. Therefore, this example involves several physics, such as the solid, the fluid, the interaction between them, and the impact between the valve and its seat. For this reason, it is an ambitious and essential example for the industry since it allows an understanding of the behavior of a valve before collapsing. Given its relevance, in this case, this example has been analyzed with the TermoFluids software, the finite element method, and the formulation presented in this thesis. Finally, the conclusions are summarized and exposed in Chapter 5(Español) Esta tesis tiene como objetivo desarrollar un método de volumenes finitos de alto orden para la dinámica de sólidos en mallas tridimensionales no estructuradas. Adoptar métodos de interpolación de alto orden tiene gran importancia en la aplicación eficiente de métodos numéricos para la resolución de problemas reales donde se produce concentración de tensiones, y ayuda a evitar la aparición del conocido efecto de bloqueo de cortante. Es posible evitar un efecto tan perjudicial sin adoptar esquemas de alto orden pero con simulaciones más costosas y complejas. Esta tesis se ha desarrollado dentro del grupo de investigación del Centro Tecnológico de Transferencia de Calor, donde el análisis estructural mediante métodos numéricos es un campo de investigación en desarrollo. Además, hasta el momento no se ha desarrollado el método de volúmenes finitos con interpolación de alto orden en mallas no estructuradas. Por lo tanto, esta tesis es el primer intento de desarrollar este tipo de metodología en la mecánica computacional de sólidos. Este trabajo se desarrolla en cinco capítulos. La introducción presenta una revisión de la bibliografía, motivaciones y objetivos. Los siguientes tres capítulos revelan, a través de diferentes ejemplos, la validación y verificación de la formulación matemática propuesta. Cabe señalar que gran parte del contenido incluido en estos tres capítulos ya ha sido presentado o publicado en revistas y congresos internacionales. Sin embargo, se han introducido algunos cambios con respecto a los documentos originales. Por ejemplo, muchas validaciones y ejemplos de verificación se crearon específicamente para esta tesis. El último capítulo resume las principales contribuciones y propone ideas para ampliar esta tesis. En detalle, este trabajo comienza presentando el desarrollo histórico del método de volúmenes finitos, presentando un ejemplo donde aparece el fenómeno de bloqueo por cortante y puede afectar la solución de problemas reales de flexión. A continuación, se muestra la formulación matemática con todos los conceptos teóricos necesarios para reproducir el método, desde conceptos básicos de mecánica de sólidos hasta la introducción de los dos métodos de interpolación adoptados: mínimos cuadrados móviles y estimadores de regresión local. Además, se presentan la discretización espacial y temporal utilizada, así como el proceso de resolución mediante el método de Newton-Raphson, y los problemas no lineales asociados a las no linealidades geométricas o materiales. Seguido a lo anterior, se lleva a cabo la verificación y validación del método presentado. Se realiza un análisis exhaustivo de todos los parámetros que intervienen en la formulación en problemas bidimensionales y tridimensionales. Asimismo, en todos los ejemplos se comparan los resultados con soluciones analíticas y con soluciones obtenidas por otros métodos. Posteriormente, se presenta el análisis de un ejemplo industrial realizado en colaboración con la empresa Voestalpine. El objetivo de esta colaboración fue caracterizar el comportamiento de la válvula de un compresor en su operación cíclica. La empresa desarrolló un banco de pruebas de fatiga por impacto, a partir del cual se obtuvieron las mediciones de desplazamiento usados para validar el método. El experimento mide el desplazamiento de la válvula a medida que el aire comprimido la abre y la cierra golpeando repetidamente el asiento. Por lo tanto, este ejemplo involucra varias físicas, como la del sólido, el fluido, la interacción entre ellos y el impacto entre la válvula y su asiento. Por ello, es un ejemplo ambicioso y fundamental para la industria ya que permite conocer el comportamiento de una válvula antes de colapsar. Dada su relevancia, en este caso se ha analizado este ejemplo con el software TermoFluids, el método de los elementos finitos y la formulación presentada en esta tesis. Finalmente, las conclusiones se resumen y exponen en el Capítulo 5.DOCTORAT EN ENGINYERIA TÈRMICA (Pla 2012

High-order finite volume method for solid dynamics in fluid-structure interaction applications

A la portada: "Centre Tecnològic de Transferència de Calor"(English) This thesis aims at developing a high-order finite volume method for solid dynamics on unstructured three-dimensional meshes. The adoption of high-order interpolation methods has a key importance in the efficient application of numerical methods for the resolution of real engineering problems where stress concentration occurs, and it helps to avoid the appearance of the well-known shear locking effect. Avoiding such a detrimental effect would be possible without adopting high-order schemes but with more costly and complex numerical simulations. This thesis has been developed within the Heat and Mass Transfer Technological Center research group, where structural analysis through numerical methods is a developing field of research. Besides, until now, there has been no development of the finite volume method with high-order interpolation on unstructured meshes. Hence, this thesis is the first attempt to develop this kind of methodology in the general field of study of computational solid mechanics. This work is developed into five chapters. The introduction presents a review of the bibliography, motivations, and objectives. The following three chapters reveal, through different examples, the validation and verification of the proposed mathematical formulation. It is worth noting that much of the content included in these three chapters has already been presented or published in international journals and conferences. However, some changes have been introduced with respect to the original documents. For instance, many validations and verification examples were created specifically for this thesis. The last chapter summarizes the main contributions and proposes ideas to expand this thesis in the future. In detail, this work starts by introducing the historical development of the finite volume method to solve solid problems, presenting an example where the shear locking phenomenon appears and may affect the solution of bending-dominant real problems. Next, the mathematical formulation is displayed with all the theoretical concepts needed to reproduce the method, from basic concepts of solid mechanics to the introduction of the two adopted interpolation methods: moving least squares and local regression estimators. In addition, the used spatial and temporal discretization are presented, as well as the resolution process through the Newton-Raphson method, and the nonlinear problems associated with geometric or material nonlinearities. Following the above, the verification and validation of the presented method are carried out. An exhaustive analysis of all the parameters involved in formulating both two-dimensional and three-dimensional problems is performed. Likewise, in all the examples, the results are compared with analytical solutions and with solutions obtained by other methods. Subsequently, the analysis of an industrial example carried out in collaboration with the Voestalpine company is presented. The objective of this collaboration was to characterize the behavior of the reed valve of a compressor in its cyclic operation. The company developed a custom-built impact fatigue test rig, from which displacement measurements were obtained and used to validate the method. The experiment measures the displacement of the valve as the compressed air opens and closes it by repeatedly hitting the seat, which leads to valve failure due to fatigue stresses. Therefore, this example involves several physics, such as the solid, the fluid, the interaction between them, and the impact between the valve and its seat. For this reason, it is an ambitious and essential example for the industry since it allows an understanding of the behavior of a valve before collapsing. Given its relevance, in this case, this example has been analyzed with the TermoFluids software, the finite element method, and the formulation presented in this thesis. Finally, the conclusions are summarized and exposed in Chapter 5(Español) Esta tesis tiene como objetivo desarrollar un método de volumenes finitos de alto orden para la dinámica de sólidos en mallas tridimensionales no estructuradas. Adoptar métodos de interpolación de alto orden tiene gran importancia en la aplicación eficiente de métodos numéricos para la resolución de problemas reales donde se produce concentración de tensiones, y ayuda a evitar la aparición del conocido efecto de bloqueo de cortante. Es posible evitar un efecto tan perjudicial sin adoptar esquemas de alto orden pero con simulaciones más costosas y complejas. Esta tesis se ha desarrollado dentro del grupo de investigación del Centro Tecnológico de Transferencia de Calor, donde el análisis estructural mediante métodos numéricos es un campo de investigación en desarrollo. Además, hasta el momento no se ha desarrollado el método de volúmenes finitos con interpolación de alto orden en mallas no estructuradas. Por lo tanto, esta tesis es el primer intento de desarrollar este tipo de metodología en la mecánica computacional de sólidos. Este trabajo se desarrolla en cinco capítulos. La introducción presenta una revisión de la bibliografía, motivaciones y objetivos. Los siguientes tres capítulos revelan, a través de diferentes ejemplos, la validación y verificación de la formulación matemática propuesta. Cabe señalar que gran parte del contenido incluido en estos tres capítulos ya ha sido presentado o publicado en revistas y congresos internacionales. Sin embargo, se han introducido algunos cambios con respecto a los documentos originales. Por ejemplo, muchas validaciones y ejemplos de verificación se crearon específicamente para esta tesis. El último capítulo resume las principales contribuciones y propone ideas para ampliar esta tesis. En detalle, este trabajo comienza presentando el desarrollo histórico del método de volúmenes finitos, presentando un ejemplo donde aparece el fenómeno de bloqueo por cortante y puede afectar la solución de problemas reales de flexión. A continuación, se muestra la formulación matemática con todos los conceptos teóricos necesarios para reproducir el método, desde conceptos básicos de mecánica de sólidos hasta la introducción de los dos métodos de interpolación adoptados: mínimos cuadrados móviles y estimadores de regresión local. Además, se presentan la discretización espacial y temporal utilizada, así como el proceso de resolución mediante el método de Newton-Raphson, y los problemas no lineales asociados a las no linealidades geométricas o materiales. Seguido a lo anterior, se lleva a cabo la verificación y validación del método presentado. Se realiza un análisis exhaustivo de todos los parámetros que intervienen en la formulación en problemas bidimensionales y tridimensionales. Asimismo, en todos los ejemplos se comparan los resultados con soluciones analíticas y con soluciones obtenidas por otros métodos. Posteriormente, se presenta el análisis de un ejemplo industrial realizado en colaboración con la empresa Voestalpine. El objetivo de esta colaboración fue caracterizar el comportamiento de la válvula de un compresor en su operación cíclica. La empresa desarrolló un banco de pruebas de fatiga por impacto, a partir del cual se obtuvieron las mediciones de desplazamiento usados para validar el método. El experimento mide el desplazamiento de la válvula a medida que el aire comprimido la abre y la cierra golpeando repetidamente el asiento. Por lo tanto, este ejemplo involucra varias físicas, como la del sólido, el fluido, la interacción entre ellos y el impacto entre la válvula y su asiento. Por ello, es un ejemplo ambicioso y fundamental para la industria ya que permite conocer el comportamiento de una válvula antes de colapsar. Dada su relevancia, en este caso se ha analizado este ejemplo con el software TermoFluids, el método de los elementos finitos y la formulación presentada en esta tesis. Finalmente, las conclusiones se resumen y exponen en el Capítulo 5.Postprint (published version

High-order cell-centered finite volume method for solid dynamics on unstructured meshes

This paper introduces a high-order finite volume method for solving solid dynamics problems on three-dimensional unstructured meshes. The method is based on truncated Taylor series constructed about each control volume face using the least squares method, extending the classical finite volume method to arbitrary interpolation orders. As verification tests, a static analytical example for small deformations, a hyperelastic cantilever beam with large deformations, and a cantilever beam subject to a dynamic load are analyzed. The results provide an optimal set of parameters for the interpolation method and allow a comparison with other classic schemes, yielding to improved results in terms of accuracy and computational cost. The final test consists in the simulation of a compressor reed valve in a dynamic scenario mimicking real-life conditions. Numerical results are compared against experimental data in terms of displacements and velocity; then, a comprehensive physical analysis of stresses, caused by bending and impact of the valve, is carried out. Overall, the method is demonstrated to be accurate and effective in handling shear locking, stress concentrations, and complex geometries and improves the effectiveness of the finite volume method for solving structural problems.The authors acknowledge Voestalpine Precision Strip AB company for the previous research collaboration project that allows to experimentally validate the numerical method presented. P. Castrillo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC (109 FPI-UPC 2018). E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060). The authors would like to thank Professor Alfredo Canelas for his support during the development of the current work.Peer ReviewedPostprint (author's final draft

Experimental and numerical analysis of reed valve movement in an impact fatigue test system and reciprocating compressors

During operation of a reciprocating compressor, its flapper valve opens to allow the passage of gases and closes by striking against the valve impact plate. This reed valve movement and impact is repeated billions of times. This cyclic movement has a significant influence on the impact fatigue life of the reed valve and, hence, the lifetime of a compressor. Inside a reciprocating compressor, a number of parameters including: the valve design, valve material, compressor operating frequency and suction/exhaust pressure, influence the reed valve movement. The valve movement can be defined in terms of valve frequency, valve lift, valve velocity and impact velocity. These response parameters heavily influence the compressor efficiency and impact fatigue life of reed valves. In this paper, we first studied the valve movement parameters for a reed valve design using an experimental test setup. In experimental testing, the valves were excited into movement using air pressure pulses at a frequency of 100 Hz (air pulse width of 5 milliseconds). The valve movement was recorded by a laser sensor at 10 000 frames per second. The operating conditions such as the operating frequency, air pulse width, applied pressure and airflow rate were measured. The valves were not tested to failure but only to collect the dynamic data of valve movement such as the valve movement curve (valve displacement vs time), average valve lift and reed velocity data. The same valve design was simulated by means of different commercial software to determine its natural modes of vibration from modal analysis. The experimental results were employed to validate a complex in-house 3D CFD finite-volume model aimed at studying in detail the valve and gas dynamics, whose interaction is solved by means of a Fluid-Structure Interaction (FSI) algorithm. The complete valve movement curve obtained from simulations – reed valve displacement vs time – correlated with that obtained from the experimental tests with small error. Similarly, the difference in experimental and numerically obtained average valve lift and impact velocity values were quite small for practical purposes. Finally, fluid-dynamic results for pressure and impact forces were employed to feed a finite-element based code aimed at studying the structural behavior of the reed vale. Bending fatigue and impact fatigue stresses induced in the reed valve during its movement cycle were calculated. The magnitude of stresses and their positioning was determined, which correlated with the commonly observed areas of fracture initiation in these valves. The numerical models, as well as the information obtained from this study will help the compressor manufacturers to design their compressors to enhance efficiency and reed valve’s reliability. This type of information is not readily available from a working compressor.This research was made possible through funding and support by voestalpine Precision Strip AB, Sweden. Special thanks is extended to our research partners in this project at Termofluids and Universitat Politècnica de Catalunya - Barcelona Tech (UPC).Postprint (published version

High-order finite volume method for linear elasticity on unstructured meshes

This paper presents a high-order finite volume method for solving linear elasticity problems on two-dimensional unstructured meshes. The method is designed to increase the effectiveness of finite volume methods in solving structural problems affected by shear locking. The particular feature of the proposed method is the use of Moving Least Squares (MLS) and Local Regression Estimators (LRE). Unlike other approaches proposed before, these interpolation schemes lead to a natural and simple extension of the classical finite volume method to arbitrary order. The unknowns of the problem are still the nodal values of the displacement which are obtained implicitly in a direct solution strategy. Some canonical tests are performed to demonstrate the accuracy of the method. An analytical example is considered to evaluate the sensitivity of the solution concerning the parameters of the algorithm. A thin curved beam and a crack problem are considered to show that the method can deal with the shear locking effect, stress concentrations, and geometries where unstructured meshes are required. An overall better behavior of the LRE is observed. A comparison between low and high-order schemes is presented, and a set of parameters for the interpolation method is found, delivering good results for the proposed cases.P. Castrillo gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC (109 FPI-UPC 2018). A. Canelas thanks the Uruguayan research councils ANII and CSIC for the financial support.Peer ReviewedPostprint (author's final draft