Pub Date : 2025-12-31DOI: 10.1016/j.camwa.2025.12.024
Zhixian Lv , Jiahao Huang , Chengyang Yue , Junseok Kim , Yibao Li
Dendritic crystal growth is a complex phenomenon that has traditionally required high-fidelity simulations, which are computationally expensive. This study introduces a data-driven reduced-order modeling framework for efficient prediction of dendritic crystal growth. A β-variational autoencoder is utilized to compress coupled physical fields into a compact latent space. We systematically evaluate the impact of the regularization parameter and latent dimensionality on reconstruction accuracy. The trained encoder-decoder pair is integrated into an end-to-end time-series forecasting framework, where multiple representative models are employed to predict future latent dynamics. We investigate the influence of input sequence length and prediction horizon on forecasting accuracy, as well as the inference efficiency of the different models. Numerical experiments on a phase-field crystal growth dataset demonstrate that the proposed approach achieves high reconstruction fidelity, robust predictive performance, and significant reduction in computational cost. This offers a practical solution for fast modeling and multi-scale dynamics prediction in complex physical systems.
{"title":"Efficient prediction of phase-field crystal dynamics via β-variational autoencoders and time-series transformers on coupled physical fields","authors":"Zhixian Lv , Jiahao Huang , Chengyang Yue , Junseok Kim , Yibao Li","doi":"10.1016/j.camwa.2025.12.024","DOIUrl":"10.1016/j.camwa.2025.12.024","url":null,"abstract":"<div><div>Dendritic crystal growth is a complex phenomenon that has traditionally required high-fidelity simulations, which are computationally expensive. This study introduces a data-driven reduced-order modeling framework for efficient prediction of dendritic crystal growth. A <em>β</em>-variational autoencoder is utilized to compress coupled physical fields into a compact latent space. We systematically evaluate the impact of the regularization parameter and latent dimensionality on reconstruction accuracy. The trained encoder-decoder pair is integrated into an end-to-end time-series forecasting framework, where multiple representative models are employed to predict future latent dynamics. We investigate the influence of input sequence length and prediction horizon on forecasting accuracy, as well as the inference efficiency of the different models. Numerical experiments on a phase-field crystal growth dataset demonstrate that the proposed approach achieves high reconstruction fidelity, robust predictive performance, and significant reduction in computational cost. This offers a practical solution for fast modeling and multi-scale dynamics prediction in complex physical systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 198-215"},"PeriodicalIF":2.5,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884878","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}
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the “full” space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach.
{"title":"Solving fluid flow problems in space-time with multiscale stabilization: Formulation and examples","authors":"Biswajit Khara , Robert Dyja , Kumar Saurabh , Anupam Sharma , Baskar Ganapathysubramanian","doi":"10.1016/j.camwa.2025.12.019","DOIUrl":"10.1016/j.camwa.2025.12.019","url":null,"abstract":"<div><div>We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the “full” space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 150-177"},"PeriodicalIF":2.5,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885775","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}
Pub Date : 2025-12-29DOI: 10.1016/j.camwa.2025.12.017
Caterina B. Leimer Saglio, Stefano Pagani, Mattia Corti, Paola F. Antonietti
Epilepsy is a neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain. This work employs the monodomain model, coupled with specific models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure, and keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes. We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an a-priori convergence analysis for a simplified mathematical problem.
{"title":"A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures","authors":"Caterina B. Leimer Saglio, Stefano Pagani, Mattia Corti, Paola F. Antonietti","doi":"10.1016/j.camwa.2025.12.017","DOIUrl":"10.1016/j.camwa.2025.12.017","url":null,"abstract":"<div><div>Epilepsy is a neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain. This work employs the monodomain model, coupled with specific models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure, and keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes. We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an <em>a-priori</em> convergence analysis for a simplified mathematical problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 112-131"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885771","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}
Pub Date : 2025-12-29DOI: 10.1016/j.camwa.2025.12.015
Baiyili Liu , Songsong Ji , Gang Pang , Shaoqiang Tang , Lei Zhang
In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections. First, we formulate the dynamic equations and calculate the dispersion relation for the harmonic honeycomb lattice, then symmetrically choose specific atoms near the boundary to design different forms of matching boundary conditions. The boundary coefficients are determined by matching a residual function at some selected wavenumbers. Several atomic simulations are performed to test the effectiveness of matching boundary conditions in the example of a harmonic honeycomb lattice and a nonlinear honeycomb lattice with the FPU-β potential. Numerical results illustrate that the low-order matching boundary conditions mainly treat long waves, while the high-order matching boundary conditions can efficiently suppress short waves and long waves simultaneously. Decaying kinetic energy curves indicate the stability of matching boundary conditions in numerical simulations.
{"title":"Efficient matching boundary conditions of two-dimensional honeycomb lattice for atomic simulations","authors":"Baiyili Liu , Songsong Ji , Gang Pang , Shaoqiang Tang , Lei Zhang","doi":"10.1016/j.camwa.2025.12.015","DOIUrl":"10.1016/j.camwa.2025.12.015","url":null,"abstract":"<div><div>In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections. First, we formulate the dynamic equations and calculate the dispersion relation for the harmonic honeycomb lattice, then symmetrically choose specific atoms near the boundary to design different forms of matching boundary conditions. The boundary coefficients are determined by matching a residual function at some selected wavenumbers. Several atomic simulations are performed to test the effectiveness of matching boundary conditions in the example of a harmonic honeycomb lattice and a nonlinear honeycomb lattice with the FPU-<em>β</em> potential. Numerical results illustrate that the low-order matching boundary conditions mainly treat long waves, while the high-order matching boundary conditions can efficiently suppress short waves and long waves simultaneously. Decaying kinetic energy curves indicate the stability of matching boundary conditions in numerical simulations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 86-111"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885773","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}
Pub Date : 2025-12-29DOI: 10.1016/j.camwa.2025.12.016
Dawei Chen, Qinzhen Ren, Minghui Li
In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments.
{"title":"New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system","authors":"Dawei Chen, Qinzhen Ren, Minghui Li","doi":"10.1016/j.camwa.2025.12.016","DOIUrl":"10.1016/j.camwa.2025.12.016","url":null,"abstract":"<div><div>In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 182-197"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884964","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}
Pub Date : 2025-12-29DOI: 10.1016/j.camwa.2025.12.006
Rui Zhang , Yu Gao
The high-frequency Helmholtz equations are extensively emerging in many fields, such as seismic wave detection, medicine, and the military. Deep neural networks have shown promise in solving differential equations, yet remain challenged by the ill-conditioning of high-frequency Helmholtz operators. To address this, we propose a Hybrid Fourier KAN-SepONet solver for high-frequency Helmholtz equations. Our approach transforms the problem into a well conditioned integral operator equation using potential theory, approximates the integral operator efficiently via SepONet, and solves it with a physics-informed Fourier KAN. We prove the reformulated equation is a second-kind Fredholm system and analyze convergence through the condition number of the training matrix. Numerical results confirm the solver’s efficiency.
{"title":"An efficient hybrid Fourier KAN-SepONet solver for the high-frequency Helmholtz equation and convergence analysis","authors":"Rui Zhang , Yu Gao","doi":"10.1016/j.camwa.2025.12.006","DOIUrl":"10.1016/j.camwa.2025.12.006","url":null,"abstract":"<div><div>The high-frequency Helmholtz equations are extensively emerging in many fields, such as seismic wave detection, medicine, and the military. Deep neural networks have shown promise in solving differential equations, yet remain challenged by the ill-conditioning of high-frequency Helmholtz operators. To address this, we propose a Hybrid Fourier KAN-SepONet solver for high-frequency Helmholtz equations. Our approach transforms the problem into a well conditioned integral operator equation using potential theory, approximates the integral operator efficiently via SepONet, and solves it with a physics-informed Fourier KAN. We prove the reformulated equation is a second-kind Fredholm system and analyze convergence through the condition number of the training matrix. Numerical results confirm the solver’s efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 162-181"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884877","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}
Pub Date : 2025-12-29DOI: 10.1016/j.camwa.2025.12.007
Yu Du , Yonglin Li , Jiwei Zhang
In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions.
{"title":"A discrete perfectly matched layer for peridynamic scalar waves in two-dimensional viscous media","authors":"Yu Du , Yonglin Li , Jiwei Zhang","doi":"10.1016/j.camwa.2025.12.007","DOIUrl":"10.1016/j.camwa.2025.12.007","url":null,"abstract":"<div><div>In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 132-149"},"PeriodicalIF":2.5,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885772","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}
Pub Date : 2025-12-27DOI: 10.1016/j.camwa.2025.12.011
Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi
The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.
{"title":"Analysis of the weighted shifted boundary method for the Poisson and Stokes problems","authors":"Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi","doi":"10.1016/j.camwa.2025.12.011","DOIUrl":"10.1016/j.camwa.2025.12.011","url":null,"abstract":"<div><div>The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly <em>shifting</em> the <em>location</em> and <em>values</em> of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; <em>L</em><sup>2</sup>-error estimates can also be derived.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 63-85"},"PeriodicalIF":2.5,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842522","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}
Pub Date : 2025-12-27DOI: 10.1016/j.camwa.2025.12.020
C Venkata Lakshmi , Anuradha Aravapalli , K Venkatadri , Hakan F. Öztop
This study investigates magnetohydrodynamic natural convection of nanofluids in a square cavity subjected to sinusoidally varying thermal boundary conditions along the bottom wall. Understanding such flows is important for applications in thermal management, energy systems, and materials processing. The problem is solved using the lattice Boltzmann method coupled with an artificial neural network model to accelerate prediction of heat transfer responses. A comprehensive parametric analysis is performed for Rayleigh numbers up to , Hartmann numbers up to 40, nanoparticle concentrations up to 4%, and a range of thermal wavelength parameters. The results show that the oscillatory thermal boundary significantly modifies flow structures and heat transfer characteristics: for example, at and τ=0.5, the average Nusselt number is enhanced by nearly 28% compared with uniform heating, while strong magnetic damping (Ha=40) reduces it by about 35%. The neural network model reproduces LBM results with prediction errors below 2%, offering rapid estimation of Nusselt numbers across the studied parameter space. The novelty of this work lies in combining a high-fidelity lattice Boltzmann solver with data-driven prediction to study magnetically controlled nanofluid convection under oscillatory heating, an area not previously addressed in the literature. These findings provide new insights into the manipulation of convective transport in multiphysics thermal systems.
{"title":"Artificial Neural Network-Based Parameter Estimation in Lattice Boltzmann Simulations of MHD Nanofluid Natural Convection with Oscillating Wall Temperature","authors":"C Venkata Lakshmi , Anuradha Aravapalli , K Venkatadri , Hakan F. Öztop","doi":"10.1016/j.camwa.2025.12.020","DOIUrl":"10.1016/j.camwa.2025.12.020","url":null,"abstract":"<div><div>This study investigates magnetohydrodynamic natural convection of nanofluids in a square cavity subjected to sinusoidally varying thermal boundary conditions along the bottom wall. Understanding such flows is important for applications in thermal management, energy systems, and materials processing. The problem is solved using the lattice Boltzmann method coupled with an artificial neural network model to accelerate prediction of heat transfer responses. A comprehensive parametric analysis is performed for Rayleigh numbers up to <span><math><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup></math></span>, Hartmann numbers up to 40, nanoparticle concentrations up to 4%, and a range of thermal wavelength parameters. The results show that the oscillatory thermal boundary significantly modifies flow structures and heat transfer characteristics: for example, at <span><math><mrow><mi>R</mi><mi>a</mi><mo>=</mo><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup></mrow></math></span> and τ=0.5, the average Nusselt number is enhanced by nearly 28% compared with uniform heating, while strong magnetic damping (Ha=40) reduces it by about 35%. The neural network model reproduces LBM results with prediction errors below 2%, offering rapid estimation of Nusselt numbers across the studied parameter space. The novelty of this work lies in combining a high-fidelity lattice Boltzmann solver with data-driven prediction to study magnetically controlled nanofluid convection under oscillatory heating, an area not previously addressed in the literature. These findings provide new insights into the manipulation of convective transport in multiphysics thermal systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 40-62"},"PeriodicalIF":2.5,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842450","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}
Pub Date : 2025-12-26DOI: 10.1016/j.camwa.2025.12.008
Bowen Ren , Jilian Wu , Ning Li , Leilei Wei
This paper firstly adopt a novel low-complexity finite element method for incompressible natural convection problems, which is based on the characteristic finite element method (CFEM) and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method effectively addresses inherent limitations of the characteristic finite element method while retaining its essential advantages. By applying the TF to postprocess solutions obtained from the first-order characteristic finite element method (CFEM-1), we achieve a non-intrusive enhancement to existing code frameworks, boosting temporal accuracy by one order. Secondly, this paper constructs two error operators without increasing complexity, thus facilitating the construction of a new adaptive algorithm conveniently. Additionally, we consturct adaptive CFEM and adaptive CFEM plus TF. Subsequently, this paper proves the unconditional stability of the constant time stepsize CFEM plus TF. Lastly, numerical experiments presented to validate the theoretical analysis and substantiate the aforementioned propositions.
{"title":"Low-cost adaptive characteristic finite element method for incompressible natural convection problems","authors":"Bowen Ren , Jilian Wu , Ning Li , Leilei Wei","doi":"10.1016/j.camwa.2025.12.008","DOIUrl":"10.1016/j.camwa.2025.12.008","url":null,"abstract":"<div><div>This paper firstly adopt a novel low-complexity finite element method for incompressible natural convection problems, which is based on the characteristic finite element method (CFEM) and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method effectively addresses inherent limitations of the characteristic finite element method while retaining its essential advantages. By applying the TF to postprocess solutions obtained from the first-order characteristic finite element method (CFEM-1), we achieve a non-intrusive enhancement to existing code frameworks, boosting temporal accuracy by one order. Secondly, this paper constructs two error operators without increasing complexity, thus facilitating the construction of a new adaptive algorithm conveniently. Additionally, we consturct adaptive CFEM and adaptive CFEM plus TF. Subsequently, this paper proves the unconditional stability of the constant time stepsize CFEM plus TF. Lastly, numerical experiments presented to validate the theoretical analysis and substantiate the aforementioned propositions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"205 ","pages":"Pages 19-39"},"PeriodicalIF":2.5,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842449","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}
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