Computers & Mathematics with Applications最新文献

{"title":"Decoupled algorithms and analyses for an advection-reaction-diffusion model with stocking and harvesting","authors":"Mayesha Sharmim Tisha ,&nbsp;Md. Kamrujjaman ,&nbsp;Muhammad Mohebujjaman ,&nbsp;Taufiquar Khan","doi":"10.1016/j.camwa.2025.03.024","DOIUrl":"10.1016/j.camwa.2025.03.024","url":null,"abstract":"<div><div>We propose a time-dependent Advection Reaction Diffusion (ARD) <em>N</em>-species competition model to investigate the Stocking and Harvesting (SH) effect on population dynamics. For ongoing analysis, we explore the outcomes of a single species and competition between two competing species in a heterogeneous environment under no-flux boundary conditions, meaning no individual can cross the boundaries. We establish results concerning the existence, uniqueness, and positivity of the solutions. As a continuation, we propose, analyze, and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled ARD <em>N</em>-species competition model with SH effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proved rigorously. We verify the predicted convergence rates of our analysis and the efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically and observe the coexistence scenario subject to optimal stocking or harvesting.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 24-47"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations","authors":"Nour-Eddine Toutlini ,&nbsp;Abdelaziz Beljadid ,&nbsp;Azzeddine Soulaïmani","doi":"10.1016/j.camwa.2025.03.011","DOIUrl":"10.1016/j.camwa.2025.03.011","url":null,"abstract":"<div><div>In this study, a semi-implicit finite element method is proposed to solve the coupled system of infiltration and solute transport in porous media. The Richards equation is used to describe unsaturated flow, while the advection-dispersion equation (ADE) is used for modeling solute transport. The proposed approach is applied to linearize the system in time, avoiding iterative processes. A free parameter is introduced to ensure the stability of the scheme. Numerical tests are conducted to analyze the accuracy of the proposed method in comparison with three second-order iterative schemes. The proposed scheme based on the optimal free parameter is accurate and efficient since it offers a considerable gain in computational time compared to the other methods. For reliability and effectiveness evaluation of the developed semi-implicit scheme, four showcase scenarios are used. The first two numerical tests focus on modeling water flow in heterogeneous medium and transient flow in variably saturated zones. The last numerical tests are carried out to simulate the salt and nitrate transport through unsaturated porous media. The simulation results are compared with reference solutions and laboratory data, and demonstrate the effectiveness of the proposed scheme in simulating infiltration and solute transport in porous media.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 106-131"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A convective Allen-Cahn model for the two- and three-dimensional shape transformations of non-contact objects","authors":"Anwen Jiang ,&nbsp;Yan Wang ,&nbsp;Fenglian Zheng ,&nbsp;Xufeng Xiao","doi":"10.1016/j.camwa.2025.03.018","DOIUrl":"10.1016/j.camwa.2025.03.018","url":null,"abstract":"<div><div>This paper proposes a shape transformation model based on the Allen-Cahn equation, and its numerical scheme. The model overcomes the limitations of previous shape transformation models by introducing a convective term, realizing a smooth and stable shape transformation when the initial shape is not in contact with the target shape. To solve the problem of high-dimensions and the complexity of nonlinear terms, the numerical scheme adopts the dimension-splitting method, which can accelerate the computation by parallel algorithm, and incorporate a first-order stabilization term to mitigate numerical instability from explicit nonlinear computations. The numerical experiments explore the effect of the attracting coefficient and illustrates the effectiveness of our method in dealing with the non-contact objects through model comparison. Finally, 2D and 3D transformations validate the robustness and effectiveness of the proposed model and algorithm.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 72-82"},"PeriodicalIF":2.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topology optimization of Stokes eigenvalues by a level set method","authors":"Jiajie Li ,&nbsp;Meizhi Qian ,&nbsp;Shengfeng Zhu","doi":"10.1016/j.camwa.2025.03.012","DOIUrl":"10.1016/j.camwa.2025.03.012","url":null,"abstract":"<div><div>We propose a level set method for a Stokes eigenvalue optimization problem. A relaxed approach is employed first to approximate the Stokes eigenvalue problem and transform the original shape optimization problem into a topology optimization model. Then the distributed shape gradient is used in numerical algorithms based on a level set method. Single-grid and efficient two-grid level set algorithms are developed for the relaxed optimization problem. A two-grid mixed finite element scheme that has reliable accuracy and asymptotically optimal convergence is shown to improve the efficiency of the Stokes eigenvalue solver. Thus, it can save computational efforts of the whole optimization algorithm. Two and three-dimensional numerical results are reported to show effectiveness and efficiency of the algorithms.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 50-71"},"PeriodicalIF":2.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integral transform technique for determining stress intensity factor in wave propagation through functionally graded piezoelectric-viscoelastic structure","authors":"Diksha ,&nbsp;Soniya Chaudhary ,&nbsp;Pawan Kumar Sharma ,&nbsp;Qasem M. Al-Mdallal","doi":"10.1016/j.camwa.2025.03.021","DOIUrl":"10.1016/j.camwa.2025.03.021","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This study employs an integral transform approach for Love wave propagation in a rotating composite structure having an interfacial crack. The structure comprises an initially stressed functionally graded piezoelectric-viscoelastic half-space bonded to a piezoelectric-viscoelastic half-space, and is subjected to anti-plane mechanical loading and in-plane electrical loading. The study focuses on two material systems: the first material system consists of Epoxy-BNKLBT and Epoxy-KNLNTS, where BNKLBT stands for &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.885&lt;/mn&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Bi&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Na&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;TiO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.05&lt;/mn&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Bi&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;K&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;TiO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.015&lt;/mn&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Bi&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Li&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;TiO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.05&lt;/mn&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;BaTiO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, and KNLNTS represents &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;K&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.475&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Na&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.475&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Li&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.05&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Nb&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.92&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Ta&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.05&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;Sb&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0.03&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;O&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, doped with &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.4&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;wt%&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;CeO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mn&gt;0.4&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;wt%&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mtext&gt;MnO&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The second material system has Epoxy-BNKLBT and Epoxy-PZT7A, where PZT7A denotes Lead Zirconate Titanate. The viscoelastic materials are modeled to reflect their complex behavior under rotational and stress conditions. The Galilean transformation is applied to convert the Cartesian coordinate system into a moving reference frame aligned with the Love wave's propagation. Employing Bessel function properties, the system is converted into a set of double integral equations and subsequently reformulated into simultaneous Fredholm integral equations. Numerical solutions to these Fredholm integral equations are employed to compute the electric displacement intensity factor and the stress intensity factor near the interfaci","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 130-154"},"PeriodicalIF":2.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semi-implicit Lax-Wendroff kinetic scheme for multi-scale phonon transport","authors":"Shuang Peng ,&nbsp;Songze Chen ,&nbsp;Hong Liang ,&nbsp;Chuang Zhang","doi":"10.1016/j.camwa.2025.03.019","DOIUrl":"10.1016/j.camwa.2025.03.019","url":null,"abstract":"<div><div>Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the ballistic to diffusive regime. The biggest innovation of the present scheme is that the finite difference method is used to solve the phonon BTE for the reconstruction of the interfacial distribution function at the half-time step, where the second-order numerical schemes are used for both the temporal and spatial discretization. Consequently, the phonon scattering and migration are coupled together within one time step, and the evolution process of phonon distribution function follows the actual physical law even if the time step is much longer than the relaxation time. Numerical results show that the present scheme could accurately predict the steady/unsteady heat conduction in solid materials from the ballistic to diffusive regime, and its time step or cell size is not limited by the relaxation time or phonon mean free path. The present work could provide a useful tool for the efficient predictions of the macroscopic spatiotemporal distributions in the multi-scale thermal engineering.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 72-84"},"PeriodicalIF":2.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A non-convex and non-smooth weighted image denoising model","authors":"Huayu Fan ,&nbsp;Qiqi Feng ,&nbsp;Rui Chen ,&nbsp;Xiangyang Cao ,&nbsp;Zhi-Feng Pang","doi":"10.1016/j.camwa.2025.03.010","DOIUrl":"10.1016/j.camwa.2025.03.010","url":null,"abstract":"<div><div>In order to provide a more effective method to describe the local structure of the degraded image and to enhance the robustness of the denoising, we propose a non-convex total variational image denoising model that combines the non-convex log function with an adaptive weighted matrix within the total variation framework. In the proposed model, the weighted matrix is capable of effectively describing the primary direction of the edge structure, based on the coupling of the gradient operator of the denoising image and the diagonal matrix. As the proposed model is a non-convex and non-smooth optimisation problem, the iterative reweighted <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> algorithm and alternating direction multiplier method are employed to decompose it into a number of readily solvable sub-problems. The results obtained from numerical experiments demonstrate that the proposed model is capable of effectively suppressing the noise while maintaining the local structure of the image.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 85-105"},"PeriodicalIF":2.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"H1− Galerkin mixed finite element method using tensor product of cubic B-splines for two-dimensional Kuramoto-Sivashinsky equation","authors":"L. Jones Tarcius Doss,&nbsp;V. Sindhujarani","doi":"10.1016/j.camwa.2025.03.009","DOIUrl":"10.1016/j.camwa.2025.03.009","url":null,"abstract":"<div><div>The two-dimensional <span><math><mo>(</mo><mn>2</mn><mi>D</mi><mo>)</mo></math></span> Kuramoto-Sivashinsky equation offers a robust framework for studying complex, chaotic, and nonlinear dynamics in various mathematical and physical contexts. Analyzing this model also provides insights into higher-dimensional spatio-temporal chaotic systems that are relevant to many fields. This article aims to solve the scalar form of the two-dimensional Kuramoto-Sivashinsky equation using the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> mixed Galerkin finite element method. By introducing an intermediate variable, the equation is transformed into a coupled system. This system is then approximated using the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> mixed Galerkin finite element method, with the tensor product of the cubic B-spline in <em>x</em> and <em>y</em> directions serving as the test and trial functions in both the semi-discrete and fully discrete schemes. In this approach, triangularization is avoided, thereby reducing the size of the stiffness matrix. In the fully discrete scheme, the time derivative is approximated using the backward Euler method. The suitable linearization method is used to simplify the nonlinear term in both schemes. The theoretical analysis yields optimal order error estimates for the scalar unknown and its flux in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>, and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms, demonstrating the accuracy, efficiency, and stability of the proposed method. Additionally, three test problems are numerically analyzed to validate these theoretical results. The chaotic behavior of the equation is analyzed, in relation to the viscosity coefficient <em>γ</em>, and is also numerically investigated using the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 19-39"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase field lattice Boltzmann method for liquid-gas flows in complex geometries with efficient and consistent wetting boundary treatment","authors":"Dmytro Sashko ,&nbsp;Travis R. Mitchell ,&nbsp;Łukasz Łaniewski-Wołłk ,&nbsp;Christopher R. Leonardi","doi":"10.1016/j.camwa.2025.03.014","DOIUrl":"10.1016/j.camwa.2025.03.014","url":null,"abstract":"<div><div>This study investigates the application of wetting boundary conditions for modelling flows in complex curved geometries, such as rough fractures. It implements and analyses two common variants of the wetting boundary condition within the three-dimensional (3D) phase field lattice Boltzmann method. It provides a straightforward and novel extension of the geometrical approach to curved three-dimensional surfaces. It additionally implements surface-energy approach. A novel interpolation-based mitigation of the staircase approximation for curved boundaries is then developed and consistently applied to both wetting boundary conditions. The objectives of simplicity and parallel compute efficiency in implementation are emphasised. Through detailed validation on a series of 3D benchmark cases involving curved surfaces, such as droplet spread on a sphere, capillary intrusion, and droplet impact on a sphere, the behaviour of the wetting boundary conditions are validated and the differences between methods are highlighted. To demonstrate the applicability of the proposed approach in complex geometries with varying surface curvatures, two-phase flow through a synthetic rough fracture is presented. The suitability of the methods for complex simulations is also verified by comparing the computational performance between all investigated methods using this fracture flow test case. The present work thus contributes to the field of multiphase flow modelling with the lattice Boltzmann method in realistic applications where addressing the impact of complex geometries is essential.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 101-129"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixed spectral element method combined with second-order time stepping schemes for a two-dimensional nonlinear fourth-order fractional diffusion equation","authors":"Jiarui Wang,&nbsp;Yining Yang,&nbsp;Hong Li,&nbsp;Yang Liu","doi":"10.1016/j.camwa.2025.03.015","DOIUrl":"10.1016/j.camwa.2025.03.015","url":null,"abstract":"<div><div>In this article, a mixed spectral element method combined with second-order time stepping schemes for solving a two-dimensional nonlinear fourth-order fractional diffusion equation is constructed. For formulating an efficient numerical scheme, an auxiliary function is introduced to transform the fourth-order fractional system into a low-order coupled system, then the time direction is discretized by second-order FBT-<em>θ</em> schemes, and the spatial direction is approximated using the Legendre mixed spectral element method (LMSEM). The stability and the optimal error estimate with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>r</mi><mo>}</mo></mrow></msup><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>r</mi></mrow></msup><mo>)</mo></math></span> for the fully discrete scheme are derived, where <em>τ</em> stands for the time step size, <em>h</em> denotes the space step size, <em>N</em> indicates the degree of the polynomial, and <em>r</em> represents the order of Sobolev space. Finally, some numerical tests are carried out to verify the theory results and the effectiveness of the developed algorithm.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 1-18"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687658","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}