Computers & Mathematics with Applications最新文献

英文中文

A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants 可溶性表面活性剂两相流的晶格玻尔兹曼和有限差分混合方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-27 DOI: 10.1016/j.camwa.2024.09.022

Yan Ba , Haihu Liu , Wenqiang Li , Wenjing Yang

A hybrid method is developed to simulate two-phase flows with soluble surfactants. In this method, the interface and bulk surfactant concentration equations of diffuse-interface form, which include source terms to consider surfactant adsorption and desorption dynamics, are solved in the entire fluid domain by the finite difference method, while two-phase flows are solved by a lattice Boltzmann color-gradient model, which can accurately simulate binary fluids with unequal densities. The flow and interface surfactant concentration fields are coupled by a modified Langmuir equation of state, which allows for surfactant concentration beyond critical micelle concentration. The capability and accuracy of the hybrid method are first validated by simulating three numerical examples, including the adsorption of bulk surfactants onto the interface of a stationary droplet, the droplet migration in a constant surfactant gradient, and the deformation of a surfactant-laden droplet in a simple shear flow, in which the numerical results are compared with theoretical solutions and available literature data. Then, the hybrid method is applied to simulate the buoyancy-driven bubble rise in a surfactant solution, in which the influence of surfactants is identified for varying wall confinement, density ratio, Eotvos number and Biot number. It is found that surfactants exhibit a retardation effect on the bubble rise due to the Marangoni stress that resists interface motion, and the retardation effect weakens as the Eotvos or Biot number increases. We further show that the weakened retardation effect at higher Biot numbers is attributed to a decreased non-uniform effect of surfactants at the interface. By comparing with the Cahn-Hilliard phase-field method, we also show that the present method conserves the mass for each fluid, improves numerical stability especially at high density ratio and Eotvos number, and does not need the selection of free parameters, thus breaking the limitations of the existing method.

本文开发了一种混合方法来模拟含有可溶性表面活性剂的两相流动。在该方法中，采用有限差分法求解整个流体域中的扩散-界面形式的界面和块体表面活性剂浓度方程，其中包括考虑表面活性剂吸附和解吸动力学的源项，同时采用晶格玻尔兹曼颜色梯度模型求解两相流，该模型可精确模拟密度不等的二元流体。流动和界面表面活性剂浓度场通过修正的朗缪尔状态方程耦合，该方程允许表面活性剂浓度超过临界胶束浓度。首先通过模拟三个数值示例验证了混合方法的能力和准确性，包括静止液滴界面上的大量表面活性剂吸附、恒定表面活性剂梯度中的液滴迁移以及简单剪切流中富含表面活性剂液滴的变形。然后，应用混合方法模拟了表面活性剂溶液中由浮力驱动的气泡上升，其中确定了表面活性剂对不同壁面约束、密度比、Eotvos 数和 Biot 数的影响。研究发现，由于马兰戈尼应力阻碍了界面运动，表面活性剂对气泡的上升产生了阻滞作用，而随着 Eotvos 或 Biot 数的增加，这种阻滞作用会减弱。我们进一步研究发现，Biot 数越高，延缓效应越弱，这是因为界面上表面活性剂的非均匀效应减弱了。通过与 Cahn-Hilliard 相场方法的比较，我们还发现本方法保留了每种流体的质量，提高了数值稳定性，尤其是在高密度比和高 Eotvos 数下，并且不需要选择自由参数，从而打破了现有方法的局限性。

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引用次数: 0

Optimized five-by-five block preconditioning for efficient GMRES convergence in curvature-based image deblurring 优化五乘五块预处理，在基于曲率的图像去模糊中实现高效的 GMRES 收敛

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-27 DOI: 10.1016/j.camwa.2024.09.026

Shahbaz Ahmad

We introduce an enhanced preconditioning technique designed to expedite the convergence of Krylov subspace methods when dealing with non-linear systems of equations featuring a block five-by-five format. This scenario often arises in the context of cell centered finite difference discretizations applied to the mean curvature based image deblurring problem. A thorough spectral analysis of the preconditioned matrices reveals a favorable eigenvalue distribution, leading to accelerated convergence of preconditioned Generalized Minimal Residual (GMRES) methods. Furthermore, we present numerical experiments to showcase the effectiveness of this preconditioner when combined with the flexible GMRES solver for addressing non-linear systems of equations originating from a image deblurring problems. Codes can be obtained at https://github.com/shahbaz1982/Preconditioning.

我们介绍了一种增强型预处理技术，旨在加快 Krylov 子空间方法在处理以块五乘五格式为特征的非线性方程组时的收敛速度。这种情况经常出现在基于平均曲率的图像去模糊问题的单元中心有限差分离散中。通过对预处理矩阵进行全面的频谱分析，我们发现了有利的特征值分布，从而加快了预处理广义最小残差（GMRES）方法的收敛速度。此外，我们还通过数值实验展示了该预处理方法与灵活的 GMRES 求解器相结合，在解决图像去模糊问题的非线性方程组时的有效性。代码可从 https://github.com/shahbaz1982/Preconditioning 获取。

引用次数: 0

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model 多尺度动力学 SIR 流行病模型的渐近保留统一气体动力学方案

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-26 DOI: 10.1016/j.camwa.2024.09.021

Xiaojing Xu , Wenjun Sun , Qi Li

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called

P P U G K S^{2 - o r d e r}

, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called

P P U G K S^{1 - o r d e r}

, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

二维空间多尺度动力学 SIR 流行病模型被广泛用于模拟传染病在人群中的传播。该方案结合了速度变量的离散序数法和空间与时间变量的有限体积法。统一气体动力学方案（UGKS）的思想用于构建需要模型形式积分解的数值边界通量。由于 SIR 模型中三个传输方程的耦合，很难获得这些积分解。我们通过单独构建通量的方式将系统解耦。然后，根据 UGKS 框架，我们可以得到方案中所需的宏观辅助量。这样，SIR 模型就可以按顺序求解了。此外，我们还可以用数值方法证明，该方案在空间和时间上都具有二阶精度。此外，它不仅可以捕捉到扩散极限方程的解，而无需考虑单元大小和时间步长与缩放参数的小相关性，还能以一种自然的方式解决双曲机制中的解。此外，还详细分析了 UGKS 的正特性，并通过添加时间步长约束条件和应用节点限制器，得到了正 UGKS，即 PPUGKS2 阶。此外，为了解除扩散机制中的时间步长约束，还提出了一种时间一阶精度的正保留 UGKS，称为 PPUGKS1-order。最后，我们还进行了一些数值测试，以验证所提方案的性能。

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引用次数: 0

Robust boundary integral equations for the solution of elastic scattering problems via Helmholtz decompositions 通过亥姆霍兹分解求解弹性散射问题的稳健边界积分方程

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-26 DOI: 10.1016/j.camwa.2024.09.013

Víctor Domínguez , Catalin Turc

Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) (Dong et al. (2021) [20]). The main appeal of this approach is that the ensuing systems of BIE feature only integral operators associated with the Helmholtz equation. However, these BIE involve non standard boundary integral operators that do not result after the application of either the Dirichlet or the Neumann trace to Helmholtz single and double layer potentials. Rather, the Helmholtz decomposition approach leads to BIE formulations of elastic scattering problems with Neumann boundary conditions that involve boundary traces of the Hessians of Helmholtz layer potential. As a consequence, the classical combined field approach applied in the framework of the Helmholtz decompositions leads to BIE formulations which, although robust, are not of the second kind. Following the regularizing methodology introduced in Boubendir et al. (2015) [6] we design and analyze novel robust Helmholtz decomposition BIE for the solution of elastic scattering that are of the second kind in the case of smooth scatterers in two dimensions. We present a variety of numerical results based on Nyström discretizations that illustrate the good performance of the second kind regularized formulations in connections to iterative solvers.

弹性场的亥姆霍兹分解为通过边界积分方程（BIE）解决线性弹性散射问题开辟了新途径（Dong 等（2021）[20]）。这种方法的主要吸引力在于随之而来的 BIE 系统只具有与亥姆霍兹方程相关的积分算子。然而，这些 BIE 涉及的非标准边界积分算子并不是在对 Helmholtz 单层和双层势应用 Dirichlet 或 Neumann 迹之后产生的。相反，亥姆霍兹分解方法导致了具有诺伊曼边界条件的弹性散射问题的 BIE 公式化，其中涉及亥姆霍兹层势赫西亚的边界迹。因此，在亥姆霍兹分解框架内应用经典的组合场方法会产生 BIE 公式，虽然稳健，但不属于第二类。按照 Boubendir 等人（2015）[6] 中介绍的正则化方法，我们设计并分析了用于解决弹性散射的新型稳健亥姆霍兹分解 BIE，这种 BIE 在二维光滑散射体情况下属于第二类。我们介绍了基于 Nyström 离散的各种数值结果，这些结果说明了第二类正则化公式与迭代求解器的良好性能。

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引用次数: 0

A mixed virtual element method for the two-dimensional Navier-Stokes equations in stream-function formulation 流函数形式的二维纳维-斯托克斯方程混合虚拟元素法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.camwa.2024.09.020

Xi Zhang , Minfu Feng

This work presents the formulation and analysis of a

H^{1} -

conforming mixed virtual element method (VEM) for the two-dimensional stationary incompressible Navier-Stokes (NS) equations in stream-function formulation. By representing the velocity field as the curl of a stream function, we recast the second-order NS system into a fourth-order nonlinear equation for the scalar stream function, inherently satisfying the incompressibility constraint. Introducing a vorticity variable enables construction of

H^{1} -

conforming VEM spaces for both stream function and vorticity and circumventing stringent

C^{1} -

continuity constraints. The proposed method provides an initial exploration of stream function-vorticity discretizations on general polygonal meshes using the flexible VEM of arbitrary order. Existence and uniqueness of discrete solutions are established theoretically under a small data assumption. Optimal error estimates are then derived in the energy norm for the stream function,

H^{1} -

norm for the stream function and

L^{2} -

norm for the vorticity, rigorously demonstrating convergence. Numerical results validate the error analysis and illustrate the accuracy and robustness of the mixed VEM for simulation of incompressible flows on complex geometries.

本研究针对流函数形式的二维静态不可压缩纳维-斯托克斯（Navier-Stokes，NS）方程，提出了一种符合 H1 的混合虚拟元素法（VEM），并对其进行了分析。通过将速度场表示为流函数的卷曲，我们将二阶 NS 系统重塑为标量流函数的四阶非线性方程，从本质上满足了不可压缩性约束。引入涡度变量可为流函数和涡度构建符合 H1 的 VEM 空间，并规避严格的 C1 连续性约束。所提出的方法初步探索了使用任意阶灵活 VEM 在一般多边形网格上进行流函数-涡度离散的方法。在小数据假设下，离散解的存在性和唯一性从理论上得以确立。然后，在流函数的能量规范、流函数的 H1- 规范和涡度的 L2- 规范中导出了最佳误差估计，并严格证明了收敛性。数值结果验证了误差分析，并说明了混合 VEM 在模拟复杂几何形状上不可压缩流动时的准确性和稳健性。

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引用次数: 0

A hybrid model for accurate prediction of composite longitudinal elastic modulus 精确预测复合材料纵向弹性模量的混合模型

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.camwa.2024.09.019

Ilige S. Hage

This research presents a novel hybrid model that integrates a physical-based empirical model with an Artificial Neural Network (ANN) to accurately predict the longitudinal modulus of elasticity for composites under compression. The study focuses on a composite material with a pore inclusion within an ABS plastic matrix, exploring various pore volumes, orientations, and shapes. As part of the proposed hybrid model, a regression-type neural network was trained in MATLAB® to predict and correct discrepancies between the Generalized Stiffness Formulation (GSF) homogenization-based modeling method and the collected compression experimental test results. Using MATLAB® neural network, random error datasets were used to train the feed-forward neural network, and the remaining error datasets were used for validating the performance of the proposed hybrid modeling scheme.

The hybrid model demonstrated superior performance, achieving the lowest Mean Error (ME) of 0.1684864, Mean Absolute Error (MAE) of 1.051846, Mean Squared Error (MSE) of 3.500952, and highest R-squared of 0.998797. The proposed hybrid model outperformed both the Generalized Stiffness Formulation (GSF) and standalone ANN models. The significant improvement in prediction accuracy underscores the novelty and robustness of the hybrid approach in composite material modeling. Furthermore, this method can be used to refine any existing physical model by focusing on improving these established models to match experimental results and reducing the discrepancies, which offers a more efficient and attractive strategy for accurate predictions.

本研究提出了一种新型混合模型，该模型将基于物理的经验模型与人工神经网络（ANN）相结合，可准确预测压缩复合材料的纵向弹性模量。研究重点是一种在 ABS 塑料基体中含有孔隙的复合材料，探讨了各种孔隙的体积、方向和形状。作为拟议混合模型的一部分，在 MATLAB® 中训练了一个回归型神经网络，用于预测和纠正基于广义刚度公式（GSF）的均质化建模方法与所收集的压缩实验测试结果之间的差异。使用 MATLAB® 神经网络，随机误差数据集用于训练前馈神经网络，其余误差数据集用于验证所提混合建模方案的性能。混合模型性能优越，平均误差 (ME) 最低，为 0.1684864；平均绝对误差 (MAE) 最低，为 1.051846；平均平方误差 (MSE) 最低，为 3.500952；R 方最高，为 0.998797。所提出的混合模型的性能优于广义刚度公式（GSF）和独立的 ANN 模型。预测精度的大幅提高凸显了混合方法在复合材料建模中的新颖性和稳健性。此外，这种方法还可用于完善任何现有的物理模型，重点是改进这些已建立的模型，使其与实验结果相匹配并减少差异，从而为精确预测提供更有效、更有吸引力的策略。

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引用次数: 0

Mathematical modeling and numerical multigoal-oriented a posteriori error control and adaptivity for a stationary, nonlinear, coupled flow temperature model with temperature dependent density 静态、非线性、密度随温度变化的耦合流动温度模型的数学建模和面向多目标的后验误差控制与适应性数值计算

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.camwa.2024.09.017

S. Beuchler , A. Demircan , B. Endtmayer , U. Morgner , T. Wick

In this work, we develop adaptive schemes using goal-oriented error control for a highly nonlinear flow temperature model with temperature dependent density. The dual-weighted residual method for computing error indicators to steer mesh refinement and solver control is employed. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.

在这项工作中，我们针对密度随温度变化的高度非线性流动温度模型，开发了采用目标导向误差控制的自适应方案。采用双加权残差法计算误差指标，以引导网格细化和求解器控制。误差指标用于采用自适应算法，并通过若干数值测试加以证实。在此过程中，误差减小和效果指数可用于确定我们框架的稳健性和效率。

引用次数: 0

A mixed immersed finite element method for fourth-order interface problems on surfaces 表面四阶界面问题的混合沉浸式有限元法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.camwa.2024.09.012

Jiaqi Chen, Xufeng Xiao, Xinlong Feng

This paper presents the first numerical attempt on fourth-order interface problems on surfaces. A mixed immersed surface finite element method based on Ciarlet-Raviart formulation is proposed for solving the problem with three types of boundary conditions. One important advantage of this method is that it can avoid the generation of complex body-fitting surface meshes. The immersed surface finite element space is given based on the mixed formulation. By modifying the representation of numerical solutions, the method is extended to solve the fourth-order interface problem with nonhomogeneous flux jump conditions. Numerical examples are given to illustrate the capabilities of the proposed method.

本文首次尝试对表面的四阶界面问题进行数值计算。本文提出了一种基于 Ciarlet-Raviart 公式的混合沉浸表面有限元方法，用于求解具有三种边界条件的问题。这种方法的一个重要优点是可以避免生成复杂的体拟合表面网格。根据混合公式给出了沉入式表面有限元空间。通过修改数值解的表示方法，该方法被扩展用于解决具有非均质通量跳跃条件的四阶界面问题。给出的数值示例说明了所提方法的能力。

引用次数: 0

A stabilizer-free weak Galerkin mixed finite element method for the biharmonic equation 双谐波方程的无稳定子弱 Galerkin 混合有限元法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-24 DOI: 10.1016/j.camwa.2024.09.011

Shanshan Gu, Fuchang Huo, Shicheng Liu

In this paper, we present and study a stabilizer-free weak Galerkin (SFWG) finite element method for the Ciarlet-Raviart mixed form of the biharmonic equation on general polygonal meshes. We utilize the SFWG solutions of the second order elliptic problem to define projection operators and build error equations. Further, using weak functions formed by discontinuous k-th order polynomials, we derive the

O (h^{k})

convergence rate for the exact solution u in the

H^{1}

norm and the

O (h^{k + 1})

convergence rate in the

L^{2}

norm. Finally, numerical examples support the results reached by the theory.

本文介绍并研究了在一般多边形网格上对双谐方程的 Ciarlet-Raviart 混合形式的无稳定子弱 Galerkin（SFWG）有限元方法。我们利用二阶椭圆问题的 SFWG 解来定义投影算子并建立误差方程。此外，利用由不连续 k 阶多项式形成的弱函数，我们得出了精确解 u 在 H1 规范下的 O(hk) 收敛率和在 L2 规范下的 O(hk+1) 收敛率。最后，数值实例支持了理论得出的结果。

引用次数: 0

On energy-consistency principle of PFM for thermal fracturing in thermoviscoelasticity solids and its application for modeling thermal response due to crack growth based on adaptive mesh technique 热弹性固体热断裂的 PFM 能量一致性原理及其在基于自适应网格技术的裂纹增长热响应建模中的应用

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2024-09-23 DOI: 10.1016/j.camwa.2024.09.016

Sayahdin Alfat

The study of thermal response in the crack tip due to crack growth is very important to study the material behavior. Actually, the thermal response in the crack tip is generated by the mechanical dissipation energy properties, e.g., the viscous energy dissipation in viscoelasticity solids. Therefore, we proposed the PFM for crack propagation in thermoviscoelasticity solids and demonstrated several numerical examples. Our present model is derived from the Francfort–Marigo energy with the Ambrosio–Tortorelli regularization, and thermal energy. Our study aims to numerically investigate the thermal response in materials due to crack growth using the proposed model. In the numerical method, we apply the adaptive finite element method because the mesh needs to be fine enough to capture the damage variable z. Several interesting numerical examples are demonstrated, such as Mode I crack propagation and scalar Mode III crack propagation in non-isothermal and adiabatic processes. Numerical experiments demonstrate the capability of the proposed model to capture the temperature increasing around crack tips which is consistent with the viewpoint of laboratory experiments in the literature.

研究裂纹生长引起的裂纹尖端热响应对研究材料行为非常重要。实际上，裂纹尖端的热响应是由机械耗散能量特性产生的，例如粘弹性固体中的粘性能量耗散。因此，我们提出了热粘弹性固体中裂纹扩展的 PFM，并演示了几个数值实例。我们目前的模型是由带有 Ambrosio-Tortorelli 正则化的 Francfort-Marigo 能量和热能导出的。我们的研究旨在利用所提出的模型对裂缝生长引起的材料热响应进行数值研究。在数值方法中，我们采用了自适应有限元方法，因为网格需要足够精细才能捕捉到损伤变量 z。我们展示了几个有趣的数值示例，如非等温和绝热过程中的模式 I 裂纹扩展和标量模式 III 裂纹扩展。数值实验证明，所提出的模型能够捕捉裂纹尖端周围的温度上升，这与文献中实验室实验的观点一致。

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引用次数: 0

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