Pub Date : 2026-01-31DOI: 10.1016/j.camwa.2026.01.034
Shougui Zhang, Cairong Li, Yulu Duan
An alternating direction method of multiplier (ADMM) based on an optimal choice of parameter is proposed for the contact problem between membranes. We use the finite-difference approximation for the problem and deduce a linear complementarity problem (LCP). Then the ADMM is employed to solve an equivalent saddle-point problem. We propose a optimal selection for the parameter, by a simple eigenvalue problem. Finally, experimental results demonstrate the theoretical analysis.
{"title":"An optimal ADMM for the contact problem between membranes","authors":"Shougui Zhang, Cairong Li, Yulu Duan","doi":"10.1016/j.camwa.2026.01.034","DOIUrl":"10.1016/j.camwa.2026.01.034","url":null,"abstract":"<div><div>An alternating direction method of multiplier (ADMM) based on an optimal choice of parameter is proposed for the contact problem between membranes. We use the finite-difference approximation for the problem and deduce a linear complementarity problem (LCP). Then the ADMM is employed to solve an equivalent saddle-point problem. We propose a optimal selection for the parameter, by a simple eigenvalue problem. Finally, experimental results demonstrate the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 334-346"},"PeriodicalIF":2.5,"publicationDate":"2026-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095741","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 : 2026-01-30DOI: 10.1016/j.camwa.2026.01.033
Ruibo Zhang , Fengjun Li , Jianqiang Liu
The Monge-Ampère equation is originated from geometric surface theory and is widely applied in optimal transport theory, image processing, optimization problem and so on. The numerical solution of the Monge-Ampère equation has recently attracted more and more attention. Physics-informed neural networks (PINNs), a new paradigm in numerical methods, introduce physical constraints during the training process so that the model not only can learn patterns in the data, but also satisfy the laws of physics. In our work, we try to solve the Monge-Ampère equation with Dirichlet boundary conditions by using the PINNs. To our knowledge, this is the first time that PINNs is applied to solve the Monge-Ampère equation. Unfortunately, the Monge-Ampère equation involves determinant calculation, which leads to calculation failure using the conventional PINNs. For this reason, inspired by the fixed-point method, we construct a Poisson series physics-informed neural networks (PS-PINNs) framework to solve this problem. The Monge-Ampère equation is transformed into a Poisson series using the fixed-point method, which avoids the direct computation of the determinant. As part of our analysis, we prove the convergence of loss function and neural networks in PS-PINNs. Moreover, we study the performance of PS-PINNs with source functions containing singularities and noise, as well as in asymmetric domains. It is worth noting that we can obtain better numerical results using a small number of sampling points and iterations. The data and code accompanying this paper are publicly available at https://github.com/RuiboZhangping/PSPINN.
{"title":"Solving the Monge-Ampère equation via Poisson series physics-informed neural networks and its convergence analysis","authors":"Ruibo Zhang , Fengjun Li , Jianqiang Liu","doi":"10.1016/j.camwa.2026.01.033","DOIUrl":"10.1016/j.camwa.2026.01.033","url":null,"abstract":"<div><div>The Monge-Ampère equation is originated from geometric surface theory and is widely applied in optimal transport theory, image processing, optimization problem and so on. The numerical solution of the Monge-Ampère equation has recently attracted more and more attention. Physics-informed neural networks (PINNs), a new paradigm in numerical methods, introduce physical constraints during the training process so that the model not only can learn patterns in the data, but also satisfy the laws of physics. In our work, we try to solve the Monge-Ampère equation with Dirichlet boundary conditions by using the PINNs. To our knowledge, this is the first time that PINNs is applied to solve the Monge-Ampère equation. Unfortunately, the Monge-Ampère equation involves determinant calculation, which leads to calculation failure using the conventional PINNs. For this reason, inspired by the fixed-point method, we construct a Poisson series physics-informed neural networks (PS-PINNs) framework to solve this problem. The Monge-Ampère equation is transformed into a Poisson series using the fixed-point method, which avoids the direct computation of the determinant. As part of our analysis, we prove the convergence of loss function and neural networks in PS-PINNs. Moreover, we study the performance of PS-PINNs with source functions containing singularities and noise, as well as in asymmetric domains. It is worth noting that we can obtain better numerical results using a small number of sampling points and iterations. The data and code accompanying this paper are publicly available at <span><span>https://github.com/RuiboZhangping/PSPINN</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 316-333"},"PeriodicalIF":2.5,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078330","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 : 2026-01-29DOI: 10.1016/j.camwa.2026.01.023
Clément Lasuen
In this paper, we propose a finite volume scheme for the linear transport equation in two space dimensions. This scheme is based on a second order upwind flux where the velocity is modified so as to recover the correct diffusion limit. A partially implicit time discretization is used. This allows to have good properties while keeping the computational cost per iteration very low. The resulting scheme is asymptotic preserving, positive under a classical CFL condition, conservative and second order consistent in all the regimes. These properties are valid on general unstructured meshes and the computational cost is similar to an explicit scheme. Eventually, the extension of this scheme to 3D unstructured meshes is straightforward and its properties remain valid.
{"title":"A positive and asymptotic preserving scheme for the linear transport equation on 2D unstructured meshes","authors":"Clément Lasuen","doi":"10.1016/j.camwa.2026.01.023","DOIUrl":"10.1016/j.camwa.2026.01.023","url":null,"abstract":"<div><div>In this paper, we propose a finite volume scheme for the linear transport equation in two space dimensions. This scheme is based on a second order upwind flux where the velocity is modified so as to recover the correct diffusion limit. A partially implicit time discretization is used. This allows to have good properties while keeping the computational cost per iteration very low. The resulting scheme is <em>asymptotic preserving</em>, positive under a classical <em>CFL</em> condition, conservative and second order consistent in all the regimes. These properties are valid on general unstructured meshes and the computational cost is similar to an explicit scheme. Eventually, the extension of this scheme to 3<em>D</em> unstructured meshes is straightforward and its properties remain valid.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 137-151"},"PeriodicalIF":2.5,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072041","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 : 2026-01-28DOI: 10.1016/j.camwa.2026.01.031
Xinkun Xiao , Qinghang Cai , Tianrui Li , Ronghua Chen , Guanghui Su
This study establishes the Moving Particle Semi-implicit Plus Uncertainty (MPSPU) framework to enable rigorous uncertainty quantification (UQ) for particle-based simulations in nuclear reactor safety analysis. Designed to extend the Best Estimate Plus Uncertainty (BEPU) methodology, MPSPU addresses the specific challenges of Lagrangian particle methods while maintaining compatibility with existing regulatory assessment protocols. The framework is validated using the SURC-4 experiment, which simulates the Molten Core–Concrete Interaction (MCCI) phenomenon. A critical advancement is the formulation of a time-dependent sensitivity analysis, which reveals that melt temperature is the dominant driver governing early-stage MCCI behavior. Furthermore, a comparative evaluation of surrogate models for MPS time-series data identifies Long Short-Term Memory (LSTM) networks as the optimal architecture, outperforming conventional polynomial and neural network approaches. To demonstrate the framework's practical utility, an end-to-end calculation example is presented, illustrating the complete workflow from raw simulation data to regulatory-grade risk metrics. This example explicitly quantifies the conditional failure probability of concrete ablation depth against safety limits, showcasing the framework's ability to support risk-informed decision-making. Ultimately, this work provides a systematic pathway for integrating particle methods into safety analysis.
{"title":"Uncertainty analysis framework of MPS and implementation in the simulation of MCCI phenomenon","authors":"Xinkun Xiao , Qinghang Cai , Tianrui Li , Ronghua Chen , Guanghui Su","doi":"10.1016/j.camwa.2026.01.031","DOIUrl":"10.1016/j.camwa.2026.01.031","url":null,"abstract":"<div><div>This study establishes the Moving Particle Semi-implicit Plus Uncertainty (MPSPU) framework to enable rigorous uncertainty quantification (UQ) for particle-based simulations in nuclear reactor safety analysis. Designed to extend the Best Estimate Plus Uncertainty (BEPU) methodology, MPSPU addresses the specific challenges of Lagrangian particle methods while maintaining compatibility with existing regulatory assessment protocols. The framework is validated using the SURC-4 experiment, which simulates the Molten Core–Concrete Interaction (MCCI) phenomenon. A critical advancement is the formulation of a time-dependent sensitivity analysis, which reveals that melt temperature is the dominant driver governing early-stage MCCI behavior. Furthermore, a comparative evaluation of surrogate models for MPS time-series data identifies Long Short-Term Memory (LSTM) networks as the optimal architecture, outperforming conventional polynomial and neural network approaches. To demonstrate the framework's practical utility, an end-to-end calculation example is presented, illustrating the complete workflow from raw simulation data to regulatory-grade risk metrics. This example explicitly quantifies the conditional failure probability of concrete ablation depth against safety limits, showcasing the framework's ability to support risk-informed decision-making. Ultimately, this work provides a systematic pathway for integrating particle methods into safety analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 116-136"},"PeriodicalIF":2.5,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072046","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}
This paper proposes a novel fractional nonlinear parabolic model based on Caputo time-fractional derivative, designed to enhance the classical Perona-Malik model for image denoising and contrast improvement. A regularized diffusion mechanism is incorporated to control the diffusion rate and direction locally. The well-posedness of the model is analyzed, and two main existence results for weak solutions are established. The first, under a bounded reaction term, is proved using Schauder’s fixed-point theorem; the second, involving a nonlinear and weakly regular source term, ensures the existence of a weak SOLA solution via approximation techniques and new technical estimates. Numerical experiments on grayscale and MRI images validate the robustness and efficiency of the proposed model under various noise levels. The results show superior denoising and enhancement performance compared to state-of-the-art methods, preserving natural appearance and minimizing artifacts. This confirms the model’s potential for high-precision image restoration applications.
{"title":"A novel evolutionary model using the Caputo time-fractional derivative and noise estimator for image denoising and contrast enhancement","authors":"Anouar Ben-Loghfyry , Abderrahim Charkaoui , Anass Bouchriti , Nour Eddine Alaa","doi":"10.1016/j.camwa.2026.01.006","DOIUrl":"10.1016/j.camwa.2026.01.006","url":null,"abstract":"<div><div>This paper proposes a novel fractional nonlinear parabolic model based on <em>Caputo</em> time-fractional derivative, designed to enhance the classical Perona-Malik model for image denoising and contrast improvement. A regularized diffusion mechanism is incorporated to control the diffusion rate and direction locally. The well-posedness of the model is analyzed, and two main existence results for weak solutions are established. The first, under a bounded reaction term, is proved using Schauder’s fixed-point theorem; the second, involving a nonlinear and weakly regular source term, ensures the existence of a weak SOLA solution via approximation techniques and new technical estimates. Numerical experiments on grayscale and MRI images validate the robustness and efficiency of the proposed model under various noise levels. The results show superior denoising and enhancement performance compared to state-of-the-art methods, preserving natural appearance and minimizing artifacts. This confirms the model’s potential for high-precision image restoration applications.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"204 ","pages":"Pages 305-346"},"PeriodicalIF":2.5,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037729","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 : 2026-01-24DOI: 10.1016/j.camwa.2026.01.024
Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha
This paper aims to study a priori error analysis of the weak Galerkin mixed finite element method (WG-MFEM) for parabolic interface problems in a two-dimensional bounded convex polygonal domain. While discontinuous functions are employed for the approximation of spatial variable, an implicit backward Euler scheme is used for the time variable. Due to the presence of the discontinuous coefficient across the interface, the solution of parabolic interface problems possesses very low global regularity. Using the Stein extension operator and the H1(div)-extension operator leads to the novel approximation results for the L2 projection operators for both the scalar and the vector-valued functions, respectively. With the help of mixed elliptic projection operator and the new approximation properties combined with the standard energy argument, an almost optimal order a priori error bounds are derived for both the solution and the flux variables in the L∞(L2) norm. Numerical outcomes for some test problems are reported to confirm the theoretical analysis.
{"title":"Error estimates of the weak Galerkin mixed finite element method for parabolic interface problems","authors":"Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha","doi":"10.1016/j.camwa.2026.01.024","DOIUrl":"10.1016/j.camwa.2026.01.024","url":null,"abstract":"<div><div>This paper aims to study a priori error analysis of the weak Galerkin mixed finite element method (WG-MFEM) for parabolic interface problems in a two-dimensional bounded convex polygonal domain. While discontinuous functions are employed for the approximation of spatial variable, an implicit backward Euler scheme is used for the time variable. Due to the presence of the discontinuous coefficient across the interface, the solution of parabolic interface problems possesses very low global regularity. Using the Stein extension operator and the <strong><em>H</em></strong><sup>1</sup>(div)-extension operator leads to the novel approximation results for the <em>L</em><sup>2</sup> projection operators for both the scalar and the vector-valued functions, respectively. With the help of mixed elliptic projection operator and the new approximation properties combined with the standard energy argument, an almost optimal order a priori error bounds are derived for both the solution and the flux variables in the <em>L</em><sup>∞</sup>(<em>L</em><sup>2</sup>) norm. Numerical outcomes for some test problems are reported to confirm the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 94-115"},"PeriodicalIF":2.5,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025840","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 : 2026-01-23DOI: 10.1016/j.camwa.2026.01.027
Eunjung Lee
Partial differential equations that exhibit reduced regularity due to geometric singularities or possess nontrivial null space components arising from intrinsic properties of the differential operator pose serious challenges for both conventional numerical methods and standard physics-informed neural networks (PINNs). Least-squares finite element methods (LSFEM) have long provided robust tools for addressing such issues through weighted norm formulations and null-space projection techniques. In this work, we propose a hybrid PINN framework that systematically incorporates key elements of LSFEM to overcome limitations of existing PINNs. By embedding weighted least-squares functionals or projection mechanisms into the PINN architecture, the proposed method effectively handles singularities and ill-posedness within a deep learning paradigm. This approach enhances solution stability, avoids pollution from singular modes, and improves accuracy in problems where standard PINNs struggle.
{"title":"Least-squares enhanced physics-informed learning for singular and ill-posed partial differential equations","authors":"Eunjung Lee","doi":"10.1016/j.camwa.2026.01.027","DOIUrl":"10.1016/j.camwa.2026.01.027","url":null,"abstract":"<div><div>Partial differential equations that exhibit reduced regularity due to geometric singularities or possess nontrivial null space components arising from intrinsic properties of the differential operator pose serious challenges for both conventional numerical methods and standard physics-informed neural networks (PINNs). Least-squares finite element methods (LSFEM) have long provided robust tools for addressing such issues through weighted norm formulations and null-space projection techniques. In this work, we propose a hybrid PINN framework that systematically incorporates key elements of LSFEM to overcome limitations of existing PINNs. By embedding weighted least-squares functionals or projection mechanisms into the PINN architecture, the proposed method effectively handles singularities and ill-posedness within a deep learning paradigm. This approach enhances solution stability, avoids pollution from singular modes, and improves accuracy in problems where standard PINNs struggle.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 301-315"},"PeriodicalIF":2.5,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033539","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 : 2026-01-23DOI: 10.1016/j.camwa.2026.01.022
Huan Wang , Naixing Feng , Chong-Zhi Han , Jinfeng Zhu , Lixia Yang , Atef Z. Elsherbeni
In this paper, the model equivalent approach is developed for full-wave analysis of electromagnetic propagation in multilayered fully anisotropic lossy media. In the process of geometric simulation, the 3D planar layered model is projected onto an axial stratified structure, effectively reducing spatial complexity. Then, the mesh free scheme is adopted for discretization, thus significantly decreasing the resource consumption. To accommodate generalized electromagnetic media, the governing equation for the electric field is formulated based on fully anisotropic media, characterized by full tensor parameters. The Galerkin method is employed to generate weak form partial differential equations (PDEs), then, the FEM is adopted to address the equations. To ensure accuracy in the FEM implementation, the divergence condition is imposed as a constraint on the PDEs, effectively eliminating spurious solutions from the computational domain. Finally, three numerical examples are presented to verify the effectiveness of the proposed method.
{"title":"EM propagation analysis of multilayered fully anisotropic media with an efficacious model equivalent approach","authors":"Huan Wang , Naixing Feng , Chong-Zhi Han , Jinfeng Zhu , Lixia Yang , Atef Z. Elsherbeni","doi":"10.1016/j.camwa.2026.01.022","DOIUrl":"10.1016/j.camwa.2026.01.022","url":null,"abstract":"<div><div>In this paper, the model equivalent approach is developed for full-wave analysis of electromagnetic propagation in multilayered fully anisotropic lossy media. In the process of geometric simulation, the 3D planar layered model is projected onto an axial stratified structure, effectively reducing spatial complexity. Then, the mesh free scheme is adopted for discretization, thus significantly decreasing the resource consumption. To accommodate generalized electromagnetic media, the governing equation for the electric field is formulated based on fully anisotropic media, characterized by full tensor parameters. The Galerkin method is employed to generate weak form partial differential equations (PDEs), then, the FEM is adopted to address the equations. To ensure accuracy in the FEM implementation, the divergence condition is imposed as a constraint on the PDEs, effectively eliminating spurious solutions from the computational domain. Finally, three numerical examples are presented to verify the effectiveness of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 79-93"},"PeriodicalIF":2.5,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025839","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}
In advanced studies of bionanoscience, magnetic nanomaterials serve as therapeutic transporters for treating vascular disorders, such as carotid and peripheral artery diseases, along with other biomedical applications. This study explores the theoretical behavior of hybrid nanoparticles (Cu-Fe2O3) in two-dimensional peristaltic blood flow through an inclined, catheterized artery, accounting for outer wall slip in an uncertain environment. The non-Newtonian Jeffrey nanofluid model is employed, incorporating nonlinear thermal radiation and an externally induced magnetic field to capture novel aspects of nanofluid behavior. However, uncertainty in velocity and temperature patterns may arise due to variations in nanoparticle volume fraction, which cannot be ignored. To address this, these distributions are analyzed within a fuzzy framework, treating them as triangular fuzzy numbers (TFNs). Within this framework, the dimensionless nonlinear flow equations are converted into fuzzy differential equations by introducing symmetrical TFNs, where the nanoparticle volume fractions serve as fuzzy parameters. The Homotopy Perturbation Method (HPM) is then applied to derive fuzzy semi analytical solutions for temperature and velocity profiles using a double parametric approach for fuzzy numbers. Additionally, a comprehensive graphical analysis is presented, incorporating triangular fuzzy representations in both two-dimensional (2D) and three-dimensional (3D) frameworks for the fuzzy solutions of temperature and velocity profiles. The obtained fuzzy solutions are validated by comparing a special case of the present solution with existing precise solutions. An in-depth analysis of key flow characteristics such as wall shear stress, the Nusselt number, and the skin friction coefficient is conducted for the special case under various emerging parameters. It is observed that as the Darcy parameter increases, both the upper and lower bounds of fuzzy velocity improve. Meanwhile, an increase in the thermal radiation parameter leads to a significant drop in the fuzzy temperature profile due to enhanced heat dissipation through radiation.
{"title":"Peristaltic transport of non-Newtonian hybrid nanofluid flow through an inclined porous tube under a magnetic field and thermal radiation in a fuzzy environment","authors":"Bivas Bhaumik , Soumini Dolui , Mrutyunjaya Sahoo , Snehashish Chakraverty , Soumen De","doi":"10.1016/j.camwa.2026.01.020","DOIUrl":"10.1016/j.camwa.2026.01.020","url":null,"abstract":"<div><div>In advanced studies of bionanoscience, magnetic nanomaterials serve as therapeutic transporters for treating vascular disorders, such as carotid and peripheral artery diseases, along with other biomedical applications. This study explores the theoretical behavior of hybrid nanoparticles (Cu-Fe<sub>2</sub>O<sub>3</sub>) in two-dimensional peristaltic blood flow through an inclined, catheterized artery, accounting for outer wall slip in an uncertain environment. The non-Newtonian Jeffrey nanofluid model is employed, incorporating nonlinear thermal radiation and an externally induced magnetic field to capture novel aspects of nanofluid behavior. However, uncertainty in velocity and temperature patterns may arise due to variations in nanoparticle volume fraction, which cannot be ignored. To address this, these distributions are analyzed within a fuzzy framework, treating them as triangular fuzzy numbers (TFNs). Within this framework, the dimensionless nonlinear flow equations are converted into fuzzy differential equations by introducing symmetrical TFNs, where the nanoparticle volume fractions serve as fuzzy parameters. The Homotopy Perturbation Method (HPM) is then applied to derive fuzzy semi analytical solutions for temperature and velocity profiles using a double parametric approach for fuzzy numbers. Additionally, a comprehensive graphical analysis is presented, incorporating triangular fuzzy representations in both two-dimensional (2D) and three-dimensional (3D) frameworks for the fuzzy solutions of temperature and velocity profiles. The obtained fuzzy solutions are validated by comparing a special case of the present solution with existing precise solutions. An in-depth analysis of key flow characteristics such as wall shear stress, the Nusselt number, and the skin friction coefficient is conducted for the special case under various emerging parameters. It is observed that as the Darcy parameter increases, both the upper and lower bounds of fuzzy velocity improve. Meanwhile, an increase in the thermal radiation parameter leads to a significant drop in the fuzzy temperature profile due to enhanced heat dissipation through radiation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 280-300"},"PeriodicalIF":2.5,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014493","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}
This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained refining the grid or increasing the polynomial degree. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy.
{"title":"A geometry aware arbitrary order collocation boundary element method solver for the potential flow past three dimensional lifting surfaces","authors":"Luca Cattarossi , Filippo Guido Davide Sacco , Nicola Giuliani , Nicola Parolini , Andrea Mola","doi":"10.1016/j.camwa.2026.01.021","DOIUrl":"10.1016/j.camwa.2026.01.021","url":null,"abstract":"<div><div>This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained refining the grid or increasing the polynomial degree. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 257-279"},"PeriodicalIF":2.5,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014794","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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