Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.193
A. Amatriain, I. Parra, G. Rubio, E. Valero
Abstract. In this work we develop a model of catheter ablation based on electromagnetic and thermal equations. This model allows the computation of the space and time evolution of temperature in the surroundings of the ablation zone. This result is relevant, as excessive temperature values may cause stream pops or esophageal ulcers. The resulting system of equations is solved using a Chebyshev spectral collocation method. Special attention is paid to the effect of blood perfusion and electrical conductivity, as there is no consensus in the literature concerning the modeling of these terms. In order to obtain the conditions that give rise to safer ablations, a parametric study is performed, where the effect of discharge time, discharge voltage and size of the electrode in the temperature distribution is analysed.
{"title":"Mathematical Modeling of Thermal Ablation Treatments in Heart Arrhythmias","authors":"A. Amatriain, I. Parra, G. Rubio, E. Valero","doi":"10.23967/WCCM-ECCOMAS.2020.193","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.193","url":null,"abstract":"Abstract. In this work we develop a model of catheter ablation based on electromagnetic and thermal equations. This model allows the computation of the space and time evolution of temperature in the surroundings of the ablation zone. This result is relevant, as excessive temperature values may cause stream pops or esophageal ulcers. The resulting system of equations is solved using a Chebyshev spectral collocation method. Special attention is paid to the effect of blood perfusion and electrical conductivity, as there is no consensus in the literature concerning the modeling of these terms. In order to obtain the conditions that give rise to safer ablations, a parametric study is performed, where the effect of discharge time, discharge voltage and size of the electrode in the temperature distribution is analysed.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124599853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.227
A. Amani, E. Schillaci, D. Kizildag, C. Pérez-Segarra
{"title":"Numerical Analysis of Viscoelastic Fluid Injection Processes","authors":"A. Amani, E. Schillaci, D. Kizildag, C. Pérez-Segarra","doi":"10.23967/WCCM-ECCOMAS.2020.227","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.227","url":null,"abstract":"","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"187 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132020371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.045
F. D. Vanna, Michele Cogo, M. Bernardini, F. Picano, E. Benini
. This present paper reports a novel methodology to simulate wall-bounded flows in the Large-Eddy Simulation framework using an automatic transition between a wall-modelled and a wall-resolved approach. The proposed technique aims at prescribing the right (modelled or resolved) wall shear stress and wall heat flux, preserving at the same time the no-slip/no-penetration conditions for the velocity and the isothermal/adiabatic conditions for the temperature fields. The approach is successfully implemented in a high-order finite-difference framework, and it is found able to adapt smoothly to the available near-wall grid spacing. Thus, the method falls into the wall-resolved case, when the near-wall dynamic is directly computed, whereas it employs the wall stress model when a full resolution of the near-wall region is not achievable. The method is tested on a nearly-incompressible turbulent channel flow and a supersonic spatially-devolving boundary layer flow. The obtained results highlight an excellent accuracy in representing the wall turbulence dynamics in terms of mean velocity profiles and fluctuations, almost independently of the near-wall spatial resolution. Thus, the proposed method results in a promising technique for analysis of high-Reynolds wall-bounded flows.
{"title":"A Wall-Modeled/Wall-Resolved LES Method For Turbulent Wall Flows","authors":"F. D. Vanna, Michele Cogo, M. Bernardini, F. Picano, E. Benini","doi":"10.23967/WCCM-ECCOMAS.2020.045","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.045","url":null,"abstract":". This present paper reports a novel methodology to simulate wall-bounded flows in the Large-Eddy Simulation framework using an automatic transition between a wall-modelled and a wall-resolved approach. The proposed technique aims at prescribing the right (modelled or resolved) wall shear stress and wall heat flux, preserving at the same time the no-slip/no-penetration conditions for the velocity and the isothermal/adiabatic conditions for the temperature fields. The approach is successfully implemented in a high-order finite-difference framework, and it is found able to adapt smoothly to the available near-wall grid spacing. Thus, the method falls into the wall-resolved case, when the near-wall dynamic is directly computed, whereas it employs the wall stress model when a full resolution of the near-wall region is not achievable. The method is tested on a nearly-incompressible turbulent channel flow and a supersonic spatially-devolving boundary layer flow. The obtained results highlight an excellent accuracy in representing the wall turbulence dynamics in terms of mean velocity profiles and fluctuations, almost independently of the near-wall spatial resolution. Thus, the proposed method results in a promising technique for analysis of high-Reynolds wall-bounded flows.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133182498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.286
A. Zemskov, D. Tarlakovskii
. We study unsteady elastic diffusion vibrations of a freely supported rectangular isotropic Kirchhoff-Love plate on an elastic foundation, which is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in multicomponent continuum is used for the mathematical problem formulation. The longitudinal and transverse vibrations equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d’Alembert variational principle. The problem solution of unsteady elastic diffusion plate vibrations is sought in integral form. The bulk Green’s functions are the kernels of the integral representations. To find the Green’s functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green’s functions in the image domain are represented in the form of rational functions depends on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The bulk Green’s functions analytical expressions are obtained. and concentration increments on time and coordinates.
{"title":"Rectangular Isotropic Kirchhoff-Love Plate on an Elastic Foundation under the Action of Unsteady Elastic Diffusion Perturbations","authors":"A. Zemskov, D. Tarlakovskii","doi":"10.23967/WCCM-ECCOMAS.2020.286","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.286","url":null,"abstract":". We study unsteady elastic diffusion vibrations of a freely supported rectangular isotropic Kirchhoff-Love plate on an elastic foundation, which is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in multicomponent continuum is used for the mathematical problem formulation. The longitudinal and transverse vibrations equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d’Alembert variational principle. The problem solution of unsteady elastic diffusion plate vibrations is sought in integral form. The bulk Green’s functions are the kernels of the integral representations. To find the Green’s functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green’s functions in the image domain are represented in the form of rational functions depends on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The bulk Green’s functions analytical expressions are obtained. and concentration increments on time and coordinates.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"168 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114372342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.010
J. Marin-Montin, F. Montero-Chacón
The performance and durability of lithium-ion batteries (LIBs) are constrained by the degradation mechanisms that take place during charge and discharge cycles. Degradation of active particles (APs) of LIBs is a complex problem involving several physical phenomena (e.g., diffusion, mechanical deformation, heat transfer, to cite a few). During lithium insertion and extraction cycles, volume changes in the AP result in high mechanical stresses and, consequently, mechanical damage that promotes capacity fade. In this work, we present a microscale 3D finite element model that takes into account the coupled effects between lithium diffusion and mechanical stress within the AP. Using the surface of an ellipsoid as the base for the geometrical construction, we are able to generate different shapes of APs, with both concave and convex surfaces. Porosity and other types of defects that may be present inside the AP are explicitly modeled, and different volume fractions, shapes, and orientations are also accounted for. In our approach, the material is discretized into a lattice of one-dimensional elements: we consider beam elements for the mechanical problem, while in the diffusive approach, the material is treated as an assembly of “nanopipes” through which the flow of Li-ions takes place. The same lattice network is used for both simulations. We follow a classical lattice model approach to characterize the fracture behavior of a single AP of a LIB anode when subjected to charge/discharge cycles. The material of the APs analyzed in this work is graphite, which presents a brittle, disordered material structure, making it suitable for lattice modeling. The mechanical problem is solved, obtaining the crack patterns associated with specific charge and discharge strategies and potential initial defects. The simulation results correctly reproduce the experimental observations on mechanical stresses and the evolution of damage. This lattice model framework analyzing the degradation in the APs of LIBs (durability) can be used to provide more information regarding the microstructural evolution, morphological changes, and mechanical degradation in APs and identify improvement strategies.
{"title":"A Coupled Diffusion-Mechanical Lattice Model for the Degradation of Graphite Active Particles of Li-Ion Battery Anodes","authors":"J. Marin-Montin, F. Montero-Chacón","doi":"10.23967/WCCM-ECCOMAS.2020.010","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.010","url":null,"abstract":"The performance and durability of lithium-ion batteries (LIBs) are constrained by the degradation mechanisms that take place during charge and discharge cycles. Degradation of active particles (APs) of LIBs is a complex problem involving several physical phenomena (e.g., diffusion, mechanical deformation, heat transfer, to cite a few). During lithium insertion and extraction cycles, volume changes in the AP result in high mechanical stresses and, consequently, mechanical damage that promotes capacity fade. In this work, we present a microscale 3D finite element model that takes into account the coupled effects between lithium diffusion and mechanical stress within the AP. Using the surface of an ellipsoid as the base for the geometrical construction, we are able to generate different shapes of APs, with both concave and convex surfaces. Porosity and other types of defects that may be present inside the AP are explicitly modeled, and different volume fractions, shapes, and orientations are also accounted for. In our approach, the material is discretized into a lattice of one-dimensional elements: we consider beam elements for the mechanical problem, while in the diffusive approach, the material is treated as an assembly of “nanopipes” through which the flow of Li-ions takes place. The same lattice network is used for both simulations. We follow a classical lattice model approach to characterize the fracture behavior of a single AP of a LIB anode when subjected to charge/discharge cycles. The material of the APs analyzed in this work is graphite, which presents a brittle, disordered material structure, making it suitable for lattice modeling. The mechanical problem is solved, obtaining the crack patterns associated with specific charge and discharge strategies and potential initial defects. The simulation results correctly reproduce the experimental observations on mechanical stresses and the evolution of damage. This lattice model framework analyzing the degradation in the APs of LIBs (durability) can be used to provide more information regarding the microstructural evolution, morphological changes, and mechanical degradation in APs and identify improvement strategies.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125087169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.351
Alessandro Della Pia, M. Chiatto, L. Luca
. Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r ρ of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as r ρ increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713 , 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.
{"title":"Unsteady Dynamics of Free-Interface Gravitational Liquid Sheet Flows","authors":"Alessandro Della Pia, M. Chiatto, L. Luca","doi":"10.23967/WCCM-ECCOMAS.2020.351","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.351","url":null,"abstract":". Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r ρ of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as r ρ increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713 , 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116756781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.240
Younghwa Cho, Rahul Bale, M. Tsubokura, N. Oshima
. In this study, we investigate grid dependency on local mesh refinement for the numerical simulation of cold flow in an aircraft engine’s fuel-injector. The numerical simulation of fully compressible Navier-Stokes equations is conducted using a hierarchical Cartesian mesh-based solver known as “CUBE”. Using the results of the high-resolution simulation as the basis, the gird dependency analysis is carried out. In addition, we evaluate the weak scaling of the underlying solver.
{"title":"Numerical Simulation of Flow in a Fuel-Injector of an Aircraft Engine Combustor Using Building-Cube Method","authors":"Younghwa Cho, Rahul Bale, M. Tsubokura, N. Oshima","doi":"10.23967/WCCM-ECCOMAS.2020.240","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.240","url":null,"abstract":". In this study, we investigate grid dependency on local mesh refinement for the numerical simulation of cold flow in an aircraft engine’s fuel-injector. The numerical simulation of fully compressible Navier-Stokes equations is conducted using a hierarchical Cartesian mesh-based solver known as “CUBE”. Using the results of the high-resolution simulation as the basis, the gird dependency analysis is carried out. In addition, we evaluate the weak scaling of the underlying solver.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"122 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129447421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.172
H. Heidarifatasmi, T. Zirwes, F. Zhang, P. Habisreuther, D. Trimis
. In this work, a hybrid Euler-Lagrangian solver for dense spray systems is developed specifically for cases where film creation by accumulation of liquid droplets at the walls plays a crucial role. Euler-Lagrangian solvers are commonly used to describe the spray with predefined spray characteristics. The Lagrangian particles represent liquid drops moving along the continuous gaseous phase. This approach assumes a small particle size compared to the cell size and it is unable to capture the breakup behavior of liquid jets in the presence of instabilities. VOF methods, on the other hand, are not a computationally feasible option when it comes to small droplet sizes as a result of liquid atomization because they have to be fully resolved by the computational mesh. Hence, multiscale simulations are required to bridge the gap between the two methods combining subgrid droplets in Lagrangian approaches and large liquid structures in VOF
{"title":"Hybrid Eulerian-Lagrangian Approach for Dense Spray Simulations","authors":"H. Heidarifatasmi, T. Zirwes, F. Zhang, P. Habisreuther, D. Trimis","doi":"10.23967/WCCM-ECCOMAS.2020.172","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.172","url":null,"abstract":". In this work, a hybrid Euler-Lagrangian solver for dense spray systems is developed specifically for cases where film creation by accumulation of liquid droplets at the walls plays a crucial role. Euler-Lagrangian solvers are commonly used to describe the spray with predefined spray characteristics. The Lagrangian particles represent liquid drops moving along the continuous gaseous phase. This approach assumes a small particle size compared to the cell size and it is unable to capture the breakup behavior of liquid jets in the presence of instabilities. VOF methods, on the other hand, are not a computationally feasible option when it comes to small droplet sizes as a result of liquid atomization because they have to be fully resolved by the computational mesh. Hence, multiscale simulations are required to bridge the gap between the two methods combining subgrid droplets in Lagrangian approaches and large liquid structures in VOF","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126825062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.318
Hugo García-Modet, L. Saucedo-Mora, Guillermo Gómez-Carano, M. Sanz-Gómez, F. Montáns
. Topology optimization has undergone tremendous development since its introduction by Bendsøe and Kikuci in 1988, especially in recent years, due to its involvement in revolutionary generative design techniques. This paper aims to lay the foundations of a generative design methodology powered by an alternative approach to the well-known density methods. Based on finite element analysis, the objective is to develop an optimization algorithm with the Young modulus of the elements as design variables. That way, while previous studies have focused on void/solid distributions, this study searches for a distribution of different E values that could be manufactured due to progress in metamaterials and additive manufacturing. A mimetic metamaterial was also developed to be coupled with the topological optimization, but will not be included in this paper. To assess the optimization algorithm, several analyses have been carried out under different load and boundary conditions. The outcome shows correlation with our initial hypothesis: elements under higher strains increase their stiffness value, while the opposite occurs for those under minor stresses. Conse-quently, the results present a structure with a Young modulus distribution that optimizes the strain energy, and therefore, reduces the displacements.
{"title":"Strain-Driven Generative Design Framework Coupled With A Mimetic Metamaterial: A Process Towards Mechanical And Shape Adaptation To Observed Structures And Functionalities","authors":"Hugo García-Modet, L. Saucedo-Mora, Guillermo Gómez-Carano, M. Sanz-Gómez, F. Montáns","doi":"10.23967/WCCM-ECCOMAS.2020.318","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.318","url":null,"abstract":". Topology optimization has undergone tremendous development since its introduction by Bendsøe and Kikuci in 1988, especially in recent years, due to its involvement in revolutionary generative design techniques. This paper aims to lay the foundations of a generative design methodology powered by an alternative approach to the well-known density methods. Based on finite element analysis, the objective is to develop an optimization algorithm with the Young modulus of the elements as design variables. That way, while previous studies have focused on void/solid distributions, this study searches for a distribution of different E values that could be manufactured due to progress in metamaterials and additive manufacturing. A mimetic metamaterial was also developed to be coupled with the topological optimization, but will not be included in this paper. To assess the optimization algorithm, several analyses have been carried out under different load and boundary conditions. The outcome shows correlation with our initial hypothesis: elements under higher strains increase their stiffness value, while the opposite occurs for those under minor stresses. Conse-quently, the results present a structure with a Young modulus distribution that optimizes the strain energy, and therefore, reduces the displacements.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131290208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-11DOI: 10.23967/WCCM-ECCOMAS.2020.221
A. Hurtado-de-Mendoza, J. Kou, S. Joshi, K. Puri, C. Hirsch, E. Ferrer
Abstract. The present study introduces an application of the non-modal analysis to multigrid operators with explicit Runge-Kutta smoothers in the context of Flux Reconstruction discretizations of the linear convection-diffusion equation. A dissipation curve is obtained that reflects upon the convergence properties of the multigrid operator. The number of smoothing steps, the type of cycle (V/W) and the combination of pand h-multigrid are taken into account in order to find those configurations which yield faster convergence rates. The analysis is carried out for polynomial orders up to P = 6, in 1D and 2D for varying degrees of convection (Péclet number), as well as for high aspect ratio cells. The non-modal analysis can support existing evidence on the behaviour of multigrid schemes. W-cycles, a higher number of coarse-level sweeps or the combined use of hp-multigrid are shown to increase the error dissipation, while higher degrees of convection and/or high aspect-ratio cells both decrease the error dissipation rate.
{"title":"Non-Modal Analysis of Multigrid Schemes for the High-Order Flux Reconstruction Method","authors":"A. Hurtado-de-Mendoza, J. Kou, S. Joshi, K. Puri, C. Hirsch, E. Ferrer","doi":"10.23967/WCCM-ECCOMAS.2020.221","DOIUrl":"https://doi.org/10.23967/WCCM-ECCOMAS.2020.221","url":null,"abstract":"Abstract. The present study introduces an application of the non-modal analysis to multigrid operators with explicit Runge-Kutta smoothers in the context of Flux Reconstruction discretizations of the linear convection-diffusion equation. A dissipation curve is obtained that reflects upon the convergence properties of the multigrid operator. The number of smoothing steps, the type of cycle (V/W) and the combination of pand h-multigrid are taken into account in order to find those configurations which yield faster convergence rates. The analysis is carried out for polynomial orders up to P = 6, in 1D and 2D for varying degrees of convection (Péclet number), as well as for high aspect ratio cells. The non-modal analysis can support existing evidence on the behaviour of multigrid schemes. W-cycles, a higher number of coarse-level sweeps or the combined use of hp-multigrid are shown to increase the error dissipation, while higher degrees of convection and/or high aspect-ratio cells both decrease the error dissipation rate.","PeriodicalId":148883,"journal":{"name":"14th WCCM-ECCOMAS Congress","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133392480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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