Computers & Mathematics with Applications最新文献

英文中文

Peristaltic transport of non-Newtonian hybrid nanofluid flow through an inclined porous tube under a magnetic field and thermal radiation in a fuzzy environment 模糊环境下磁场和热辐射作用下非牛顿混合纳米流体流过倾斜多孔管的蠕动输运

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-21 DOI: 10.1016/j.camwa.2026.01.020

Bivas Bhaumik , Soumini Dolui , Mrutyunjaya Sahoo , Snehashish Chakraverty , Soumen De

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.

在生物纳米科学的高级研究中，磁性纳米材料作为治疗性转运体用于治疗血管疾病，如颈动脉和外周动脉疾病，以及其他生物医学应用。本研究探讨了混合纳米粒子（Cu-Fe2O3）在二维蠕动血液流过倾斜导管动脉时的理论行为，考虑了不确定环境下外壁滑移的影响。采用非牛顿杰弗里纳米流体模型，结合非线性热辐射和外部感应磁场来捕捉纳米流体行为的新方面。然而，由于纳米颗粒体积分数的变化，速度和温度模式的不确定性可能会产生，这是不可忽视的。为了解决这个问题，在模糊框架内分析这些分布，将它们视为三角模糊数（tfn）。在此框架内，通过引入对称tfn将无量纲非线性流动方程转换为模糊微分方程，其中纳米颗粒体积分数作为模糊参数。然后应用同伦摄动法（HPM）对模糊数采用双参数方法推导温度和速度曲线的模糊半解析解。此外，还提出了一个全面的图形分析，在二维（2D）和三维（3D）框架中结合三角形模糊表示来获得温度和速度剖面的模糊解。通过与已有精确解的比较，验证了所得到的模糊解的正确性。针对各种新出现参数下的特殊情况，深入分析了壁面剪应力、努塞尔数、表面摩擦系数等关键流动特性。观察到，随着Darcy参数的增大，模糊速度的上界和下界都增大。同时，随着热辐射参数的增大，由于辐射散热增强，模糊温度廓线明显下降。

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引用次数: 0

Modified quadrature method for solving three-dimensional axisymmetric boundary integral equations based on two extrapolations 基于两次外推的求解三维轴对称边界积分方程的改进正交法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-02 DOI: 10.1016/j.camwa.2025.12.028

Hu Li , Jin Huang , Yanying Ma

This paper study the numerical solutions for three-dimensional axisymmetric boundary integral equations. First, a quadrature method achieving O(h³) accuracy with low computational complexity is developed. Convergence is proven using the compact operator theory. An error analysis yields a single-parameter asymptotic expansion with odd powers, enabling the creation of extrapolation algorithms to enhance accuracy. After one extrapolation, accuracy improves to O(h⁵), and further improvements are possible with using extrapolation again. Three numerical examples illustrate the algorithm’s efficiency.

本文研究了三维轴对称边界积分方程的数值解。首先，提出了一种精度为0 （h3）且计算复杂度较低的正交方法。利用紧算子理论证明了该算法的收敛性。误差分析产生单参数奇次渐近展开式，使外推算法的创建能够提高精度。在一次外推后，精度提高到0 (h5)，并且再次使用外推可以进一步提高精度。三个算例说明了该算法的有效性。

引用次数: 0

Two unconditionally energy stable schemes for the Cahn-Hilliard equation Cahn-Hilliard方程的两种无条件能量稳定格式

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-05 DOI: 10.1016/j.camwa.2025.12.010

Jie Zhou , Xuelian Jiang , Ying Liu

In this paper, we propose two fully discrete convex splitting schemes to solve the Cahn-Hilliard equation based on the mixed finite element method. For these two numerical schemes, the first-order backward Euler method and the second-order backward differentiation formula (BDF2) are used for temporal discretization, and the nonlinear term is treated by the convex splitting method. In order to ensure unconditional energy stability, the second-order time scheme requires the addition of a stability term

- β τ Δ (φ_{h}^{m + 1} - φ_{h}^{m})

, where β ≥ 0 is a stable parameter. We strictly prove that both numerical schemes have unconditional energy stability. In particular, the second-order time scheme can be guaranteed to be unconditionally energy stable for

β \geq \frac{1}{16}

. Additionally, we conduct rigorous error analysis on these two numerical schemes and obtain optimal error estimates in H₁ norm. Lastly, we verify the effectiveness of both numerical schemes and confirm the correctness of the theoretical results.

本文提出了基于混合有限元法求解Cahn-Hilliard方程的两种完全离散凸分裂格式。对于这两种数值格式，采用一阶后向欧拉法和二阶后向微分公式（BDF2）进行时间离散化，非线性项采用凸分裂法处理。为了保证能量的无条件稳定，二阶时间方案需要增加稳定项−βτΔ（φhm+1−φhm），其中β ≥ 0为稳定参数。严格证明了这两种数值格式具有无条件的能量稳定性。特别是当β≥116时，二阶时间格式可以保证无条件能量稳定。此外，我们对这两种数值格式进行了严格的误差分析，得到了H1范数下的最优误差估计。最后，我们验证了两种数值格式的有效性，并验证了理论结果的正确性。

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引用次数: 0

First- and second-order accurate, unconditionally energy gradient stable, uniquely solvable, and mass-preserving linear numerical schemes for Cahn–Hilliard equation with source term 具有源项的Cahn-Hilliard方程的一、二阶精确、无条件能量梯度稳定、唯一可解、质量保持的线性数值格式

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-02 DOI: 10.1016/j.camwa.2025.12.018

Gyeonggyu Lee , Seunggyu Lee

The Cahn–Hilliard equation describes the phase separation phenomena at the microscale, such as those observed for diblock copolymers. However, its standard form is limited to capturing diverse real-world behaviors. To address this issue, we propose a structure-preserving Cahn–Hilliard equation with a generalized source term. Based on the total energy of the suggested total energy functional, the schemes were constructed using a linearly stabilized splitting method and a fast Fourier transform. A second-order extension was achieved using the implicit-explicit Runge–Kutta method. We prove the unique solvability, mass conservation, and energy gradient stability of both first- and second-order schemes. Temporal accuracy was validated through convergence tests. Numerical experiments further illustrate the phase behaviors under varying source term orders.

Cahn-Hilliard方程描述了微观尺度上的相分离现象，如对二嵌段共聚物的观察。然而，它的标准形式仅限于捕捉各种现实世界的行为。为了解决这个问题，我们提出了一个具有广义源项的保结构Cahn-Hilliard方程。基于建议的总能量泛函的总能量，采用线性稳定分裂方法和快速傅里叶变换构造了这些格式。利用隐式-显式龙格-库塔方法实现了二阶扩展。我们证明了一阶和二阶格式的唯一可解性、质量守恒性和能量梯度稳定性。通过收敛性测试验证了时间精度。数值实验进一步说明了不同源项阶数下的相行为。

引用次数: 0

Mixed finite element method for a system of hemivariational inequalities of Navier-Stokes equations coupled with the heat equation Navier-Stokes方程与热方程耦合的半变分不等式系统的混合有限元方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.013

Hailing Xuan , Wensi Wang , Xiaoliang Cheng

This paper explores a mixed finite element method for a system of hemivariational inequalities arising from the stationary Navier-Stokes equations coupled with the heat equation. The hemivariational inequalities system models the motion of a viscous incompressible fluid with thermal effects, where both the boundary conditions for the velocity and temperature fields involve the generalized Clarke gradient. We discuss the equivalence between different variational formulations and establish an existence theorem based on an alternative iterative approach and some results on hemivariational inequalities. The Navier-Stokes hemivariational inequalities system is solved using the mixed finite element method, and corresponding error estimates are derived. Numerical outcomes are presented based on the Uzawa method, which illustrates the optimal convergence rate as indicated by the error analysis.

本文探讨了求解由稳态Navier-Stokes方程与热方程耦合引起的半变分不等式系统的混合有限元方法。半变分不等式系统模拟了具有热效应的粘性不可压缩流体的运动，其中速度场和温度场的边界条件都涉及广义Clarke梯度。本文讨论了不同变分形式之间的等价性，并基于一种可选迭代方法和关于半变分不等式的一些结果，建立了一个存在性定理。采用混合有限元法求解了Navier-Stokes半变不等式系统，并给出了相应的误差估计。给出了基于Uzawa方法的数值结果，并通过误差分析说明了该方法的最优收敛速度。

引用次数: 0

An optimal ADMM for the contact problem between membranes 膜间接触问题的最佳ADMM

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-31 DOI: 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.

针对膜间接触问题，提出了一种基于参数优化选择的交替方向乘法器（ADMM）。我们利用有限差分逼近的方法，推导出一个线性互补问题。然后利用ADMM求解等效鞍点问题。我们提出了一个参数的最优选择，通过一个简单的特征值问题。最后，实验结果验证了理论分析。

引用次数: 0

A family of upwind high-order finite volume methods for convection-diffusion problems on rectangular meshes 矩形网格对流扩散问题的迎风高阶有限体积法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-07 DOI: 10.1016/j.camwa.2025.12.023

Renhui Teng , Yonghai Li , Hongtao Yang , Qin Zhou , Xia Cui

We construct and analyze a family of upwind high-order finite volume schemes for convection-diffusion problems on rectangular meshes. The novelty is that for the upwind discretization of the convection term, we replace the trial function restricted to the dual boundary closest to the upstream element with the extension of the trial function from the upstream element. We prove coercivity and provide optimal error estimates in the H¹ and L² norms. The schemes achieve optimal convergence rates of order k in the H¹ norm and

k + 1

in the L² norm, whether in diffusion-dominated or convection-dominated regimes. Numerical experiments confirm the theoretical results.

本文构造并分析了矩形网格上对流扩散问题的一组迎风高阶有限体积格式。新颖之处在于，对于对流项的逆风离散，我们将限制在最靠近上游元素的对偶边界上的试函数替换为从上游元素扩展出来的试函数。我们证明了矫顽力，并提供了H1和L2范数的最优误差估计。无论在扩散主导还是对流主导的情况下，该方案在H1范数和L2范数上都实现了k阶和k+1阶的最优收敛速率。数值实验证实了理论结果。

引用次数: 0

On the numerical solution of high-dimensional PDEs arising in multi-asset options via a kernel-type solver 基于核解的多资产期权高维偏微分方程数值解

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-08 DOI: 10.1016/j.camwa.2025.12.027

Yanlai Song

In this study, we present a numerical framework founded on a specialized version of radial basis function-produced finite difference solvers, designed for application in both interpolation tasks and the computational solution of higher-dimensional PDEs arising in multi-asset options. The distinguishing feature of the proposed method lies in its utilization of integrated forms of a special power of the multiquadric kernel to construct novel derivative weights, thereby enhancing solution accuracy and robustness. The derivative approximations are obtained through the derivation of analytical expressions, which are then evaluated on stencils comprising both uniformly spaced and non-uniformly distributed nodes. These formulations are constructed to offer greater flexibility in handling a wide spectrum of discretization patterns. Numerical results are provided to support the theoretical discussions.

在这项研究中，我们提出了一个基于径向基函数生成的有限差分解的专门版本的数值框架，该框架旨在应用于插值任务和多资产选项中出现的高维偏微分方程的计算解决方案。该方法的显著特点在于利用多次二次核的特殊幂的积分形式来构造新的导数权值，从而提高了解的精度和鲁棒性。通过解析表达式的推导得到导数近似，然后在包含均匀分布和非均匀分布节点的模板上求值。这些公式的构造是为了在处理广泛的离散化模式时提供更大的灵活性。数值结果支持了理论讨论。

引用次数: 0

A FE-MIFVE method for three-dimensional (3D) elliptic interface problems 三维椭圆界面问题的FE-MIFVE方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-12 DOI: 10.1016/j.camwa.2026.01.003

Quanxiang Wang , Jianqiang Xie , Yu Zheng , Liqun Wang

In this paper, we propose a FE-MIFVE method for the solution of the three-dimensional elliptic interface problems on structured grids. The method uses the standard finite element discretization on regular elements, and uses the modified immersed finite volume element discretization on interface elements. By designing a suitable function which has the same jumps as the solution, we turn the original elliptic interface problem with nonhomogeneous jump conditions to be an elliptic interface problem with homogeneous jump conditions. Numerical experiments for various problems show the new proposed FE-MIFVE method can serve as an efficient field solver in a simulation on structured grids, such as predicting the electrostatics of solvated biomolecules.

本文提出了一种求解结构网格上三维椭圆界面问题的FE-MIFVE方法。该方法对规则单元采用标准有限元离散，对界面单元采用改进的浸入式有限体积单元离散。通过设计一个与解具有相同跳变的合适函数，将原具有非齐次跳变条件的椭圆界面问题转化为具有齐次跳变条件的椭圆界面问题。各种问题的数值实验表明，新提出的FE-MIFVE方法可以作为一种有效的现场求解器，用于结构化网格的模拟，如预测溶剂化生物分子的静电。

引用次数: 0

A geometry aware arbitrary order collocation boundary element method solver for the potential flow past three dimensional lifting surfaces 三维升力面势流的几何感知任意阶配置边界元法求解

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-15 Epub Date: 2026-01-21 DOI: 10.1016/j.camwa.2026.01.021

Luca Cattarossi , Filippo Guido Davide Sacco , Nicola Giuliani , Nicola Parolini , Andrea Mola

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.

本文提出了一个三维升力面势流的数值模拟模型。求解方法基于配置边界元法，结合后缘非线性库塔条件的伽辽金变分公式。类似的伽辽金变分公式也用于计算尾迹配点处的流体速度，这是使尾迹与局部流动对齐的松弛算法所要求的。这种技术的使用，通常与有限元法相关联，实际上允许以一种独立于局部网格拓扑结构的方式评估解的导数。由于这种选择，结合与CAD曲面的直接接口，求解器能够在自动细化的网格上使用任意阶的拉格朗日元素。给出了NACA 0012翼型截面矩形机翼的数值计算结果，比较了细化网格和增加多项式度所获得的精度改进。最后，对NACA 0012翼型截面矩形翼和后掠翼的数值计算结果证实了该模型能够较好地再现实验数据。

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