Computers & Mathematics with Applications最新文献

{"title":"Numerical study of magnesium dendrite microstructure under convection: Change of dendrite symmetry","authors":"Ang Zhang ,&nbsp;Minghang Yang ,&nbsp;Lang Qin ,&nbsp;Jing Cheng ,&nbsp;Yuchen Tang ,&nbsp;Jinglian Du ,&nbsp;Wenbo Yu ,&nbsp;Zhihua Dong ,&nbsp;Feng Liu ,&nbsp;Bin Jiang ,&nbsp;Fusheng Pan","doi":"10.1016/j.camwa.2024.10.038","DOIUrl":"10.1016/j.camwa.2024.10.038","url":null,"abstract":"<div><div>Besides diffusion and capillary, convection which is unavoidable under terrestrial condition has remarkable effects on the microstructure evolution during solidification. In this study, a phase-field lattice-Boltzmann model, accelerated by state-of-the-art parallel-adaptive mesh refinement algorithm, is solved to investigate the morphological evolution of the Mg-Gd dendrite under convection. The lengths of the dendrite primary arms are quantified to analyze the asymmetric dendrite patterns under convection. The effects of the multiple factors including the orientation angle, the flow intensity, and the undercooling are elucidated, and the relation between the length ratios and the three independent factors is established through multiple regression analysis. The upstream-downstream arm length difference and the included angle between the primary arms are characterized to illustrate the effect of convection on the evolution of the Mg-Gd dendrite. The 3D morphological selection, together with algorithm performance tests, is further discussed to elucidate the change of morphological symmetry under different growth conditions and to demonstrate the robustness of the numerical scheme. Deep understanding of the synergy between convection-induced solute transport and undercooling-driven growth, which largely determines the morphological selection, can assist guidance for the prediction and control of the magnesium alloy microstructures.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An implementation of hp-FEM for the fractional Laplacian","authors":"Björn Bahr,&nbsp;Markus Faustmann,&nbsp;Jens Markus Melenk","doi":"10.1016/j.camwa.2024.10.005","DOIUrl":"10.1016/j.camwa.2024.10.005","url":null,"abstract":"<div><div>We consider the discretization of the 1<em>d</em>-integral Dirichlet fractional Laplacian by <em>hp</em>-finite elements. We present quadrature schemes to set up the stiffness matrix and load vector that preserve the exponential convergence of <em>hp</em>-FEM on geometric meshes. The schemes are based on Gauss-Jacobi and Gauss-Legendre rules. We show that taking a number of quadrature points slightly exceeding the polynomial degree is enough to preserve root exponential convergence. The total number of algebraic operations to set up the system is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span>, where <em>N</em> is the problem size. Numerical examples illustrate the analysis. We also extend our analysis to the fractional Laplacian in higher dimensions for <em>hp</em>-finite element spaces based on shape regular meshes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topology optimization design of labyrinth seal-type devices considering subsonic compressible turbulent flow conditions","authors":"Luís F.N. Sá ,&nbsp;Felipe Silva Maffei ,&nbsp;Lucas N.B.S. Ribeiro ,&nbsp;Julio Romano Meneghini ,&nbsp;Emílio Carlos Nelli Silva","doi":"10.1016/j.camwa.2024.10.029","DOIUrl":"10.1016/j.camwa.2024.10.029","url":null,"abstract":"<div><div>In this work, a topology optimization model for designing devices that operate with multiple relative velocities considering turbulent compressible flows is proposed. The model consists of the Favre-averaged Navier-stokes equations in an axisymmetric domain coupled with a continuous boundary propagation model. The propagation is used to impose different solid behaviors based on which wall it is connected to, for example, solid material in contact with a rotating shaft will have a rotational velocity, while material encrusted in the support will have zero absolute velocity. The implementation is composed of a segregated solver with steps for the FANS equations, the <span><math><mi>k</mi><mo>−</mo><mi>ϵ</mi></math></span> turbulent equations, and the propagation model. The sensitivity is obtained with automatic differentiation of the adjoint method and an internal point optimizer is used to update the design variable. A study case of a labyrinth seal is defined to illustrate the methodology by using three different objective functions, maximization of radial velocity, static pressure change rate, and vorticity. The results are designs for small-scale labyrinth seals in real operation conditions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An implicit GNN solver for Poisson-like problems","authors":"Matthieu Nastorg ,&nbsp;Michele-Alessandro Bucci ,&nbsp;Thibault Faney ,&nbsp;Jean-Marc Gratien ,&nbsp;Guillaume Charpiat ,&nbsp;Marc Schoenauer","doi":"10.1016/j.camwa.2024.10.036","DOIUrl":"10.1016/j.camwa.2024.10.036","url":null,"abstract":"<div><div>This paper presents Ψ-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems on general unstructured meshes with mixed boundary conditions. By leveraging the Implicit Layer Theory, Ψ-GNN models an “infinitely” deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical pre-requisite for physical applications, and is able to adapt to any initially provided solution. Ψ-GNN is trained using a physics-informed loss, and the training process is stable by design. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, Ψ-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modular parametric PGD enabling online solution of partial differential equations","authors":"Angelo Pasquale ,&nbsp;Mohammad-Javad Kazemzadeh-Parsi ,&nbsp;Daniele Di Lorenzo ,&nbsp;Victor Champaney ,&nbsp;Amine Ammar ,&nbsp;Francisco Chinesta","doi":"10.1016/j.camwa.2024.10.037","DOIUrl":"10.1016/j.camwa.2024.10.037","url":null,"abstract":"<div><div>In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline–online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating the impact of vessel geometry on cerebral aneurysm formation using multi-phase blood flow models","authors":"Dimitrios S. Lampropoulos,&nbsp;Maria Hadjinicolaou","doi":"10.1016/j.camwa.2024.10.039","DOIUrl":"10.1016/j.camwa.2024.10.039","url":null,"abstract":"<div><div>Cerebral aneurysms represent a life-threatening condition associated with considerable morbidity and mortality rates. The formation of cerebral aneurysms is influenced by various factors, including vessel geometry, blood flow characteristics, and hemodynamic forces. In this study, we investigate the impact of vessel geometry on the formation of cerebral aneurysms utilizing computational fluid dynamics (CFD) simulations for multi-phase blood flow models.</div><div>More precisely, we employ the Finite Volume Method to numerically solve the Navier-Stokes equations for simulating blood flow. To accurately capture the intricate nature of blood behavior, we utilize a multiphase blood flow model, as blood consists of red blood cells, white blood cells, and platelets suspended in the blood plasma.</div><div>Our results demonstrate that the local curvature of the vessel has a pronounced effect on the blood flow patterns and hemodynamic forces within the vessel. Specifically, our simulations indicate that an increase in vessel curvature can lead to the formation of regions of high stress and flow stagnation, both of which are known to be associated with an increased risk of aneurysm formation.</div><div>The current study provides significant insights into the impact of vessel geometry on the formation of cerebral aneurysms. The obtained results may aid in designing treatment and preventive strategies for cerebral aneurysms, while also contributing to the existing body of knowledge on the subject. Additionally, the approach developed in this study can be applied to investigate various other vascular pathologies, including arterial stenosis and atherosclerosis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Developing PDE-constrained optimal control of multicomponent contamination flows in porous media","authors":"Khan Enaet Hossain,&nbsp;Dong Liang,&nbsp;Hongmei Zhu","doi":"10.1016/j.camwa.2024.10.033","DOIUrl":"10.1016/j.camwa.2024.10.033","url":null,"abstract":"<div><div>This paper develops a robust and efficient PDE-constrained optimal control model for multicomponent pollutions in porous media, which takes into account nonlinear multi-component contamination flows of groundwater. The objective of the pollution optimal control is to identify the optimal injection rates from the top part boundary of domain, which can minimize the least squares error between the concentrations that are simulated and the allowable observed concentrations at observation sites, combining with the affection of costs associated with reducing emissions at injection locations. To discrete the constrained governing system of nonlinear multi-component flows, the splitting improved upwind finite difference scheme is developed for multicomponent PDEs system involving nonlinear chemical reactions of multicomponent pollutants and the pollutant injected rates on the upper part boundary. We employ the differential evolution (DE) optimization algorithm to solve the optimization. We numerically demonstrate the effectiveness of our model by analyzing the flow simulation on a simple geometric aquifer and identifying the optimal injection rates by minimizing the concentration derivation and the abatement costs. We also investigate the simulation of the contamination flow in a more realistic-shaped aquifer, which further validates our model's robustness and efficacy. The developed PDE-constrained control model and algorithm can be applied to applications of groundwater pollution control.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows: For Maxwell boundary model","authors":"Jianfeng Chen ,&nbsp;Sha Liu ,&nbsp;Yong Wang ,&nbsp;Congshan Zhuo ,&nbsp;Yanguang Yang ,&nbsp;Chengwen Zhong","doi":"10.1016/j.camwa.2024.10.034","DOIUrl":"10.1016/j.camwa.2024.10.034","url":null,"abstract":"<div><div>The discrete velocity method (DVM) for rarefied flows and the unified methods (based on the DVM framework) for flows in all regimes, from continuum one to free molecular one, have worked well as precise flow solvers over the past decades and have been successfully extended to other important physical fields. Both DVM and unified methods endeavor to model the gas-gas interaction physically. However, for the gas-surface interaction (GSI) at the wall boundary, they have only use the full accommodation boundary up to now, which can be viewed as a rough Maxwell boundary with a fixed accommodation coefficient (AC) at unity, deviating from the real value. For example, the AC for metal materials typically falls in the range of 0.8 to 0.9. To overcome this bottleneck and extend the DVM and unified methods to more physical boundary conditions, an algorithm for Maxwell boundary with an adjustable AC is established into the DVM framework. The Maxwell boundary model splits the distribution of the bounce-back molecules into specular ones and Maxwellian (normal) ones. Since the bounce-back molecules after the spectral reflection does not math with the discrete velocity space (DVS), both macroscopic conservation (from numerical quadrature) and microscopic consistency in the DVS are hard to achieve in the DVM framework. In this work, this problem is addressed by employing a combination of interpolation methods for mismatch points in DVS and an efficient numerical error correction method for micro-macro consistency. On the other hand, the current Maxwell boundary for DVM takes the generality into consideration, accommodating both the recently developed efficient unstructured velocity space and the traditional Cartesian velocity space. Moreover, the proposed algorithm allows for calculations of both monatomic gases and diatomic gases with internal degrees in DVS. Finally, by being integrated with the unified gas-kinetic scheme within the DVM framework, the performance of the present GSI algorithm is validated through a series of benchmark numerical tests across a wide range of Knudsen numbers.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical and numerical analysis of reduced order interface conditions and augmented finite elements for mixed dimensional problems","authors":"Muriel Boulakia ,&nbsp;Céline Grandmont ,&nbsp;Fabien Lespagnol ,&nbsp;Paolo Zunino","doi":"10.1016/j.camwa.2024.10.028","DOIUrl":"10.1016/j.camwa.2024.10.028","url":null,"abstract":"<div><div>In this paper, we are interested in the mathematical properties of methods based on a fictitious domain approach combined with reduced-order interface coupling conditions, which have been recently introduced to simulate 3D-1D fluid-structure or structure-structure coupled problems. To give insights on the approximation properties of these methods, we investigate them in a simplified setting by considering the Poisson problem in a two-dimensional domain with non-homogeneous Dirichlet boundary conditions on small inclusions. The approximated reduced problem is obtained using a fictitious domain approach combined with a projection on a Fourier finite-dimensional space of the Lagrange multiplier associated to the Dirichlet boundary constraints, obtaining in this way a Poisson problem with defective interface conditions. After analyzing the existence of a solution of the reduced problem, we prove its convergence towards the original full problem, when the size of the holes tends towards zero, with a rate which depends on the number of modes of the finite-dimensional space. In particular, our estimates highlight the fact that to obtain a good convergence on the Lagrange multiplier, one needs to consider more modes than the first Fourier mode (constant mode). This is a key issue when one wants to deal with real coupled problems, such as fluid-structure problems for instance. Next, the numerical discretization of the reduced problem using the finite element method is analyzed in the case where the computational mesh does not fit the small inclusion interface. As is standard for these types of problem, the convergence of the solution is not optimal due to the lack of regularity of the solution. Moreover, convergence exhibits a well-known locking effect when the mesh size and the inclusion size are of the same order of magnitude. This locking effect is more apparent when increasing the number of modes and affects the Lagrange multiplier convergence rate more heavily. To resolve these issues, we propose and analyze a stabilized method and an enriched method for which additional basis functions are added without changing the approximation space of the Lagrange multiplier. Finally, the properties of numerical strategies are illustrated by numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A nonconforming extended virtual element method for Stokes interface problems","authors":"Yuxiang Huang ,&nbsp;Feng Wang ,&nbsp;Jinru Chen","doi":"10.1016/j.camwa.2024.10.027","DOIUrl":"10.1016/j.camwa.2024.10.027","url":null,"abstract":"<div><div>In this paper, we propose a nonconforming extended virtual element method, which combines the extended finite element method with the nonconforming virtual element method, for solving Stokes interface problems with the unfitted-interface mesh. By introducing some stabilization terms and penalty terms, as well as some special terms defined on non-cut edges of interface elements in the discrete bilinear form, we prove the discrete inf-sup condition and obtain optimal error estimates. It is shown that all results are not only independent of the mesh size and the viscosity coefficient, but also the interface position. Numerical experiments are performed to verify theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}