Computers & Mathematics with Applications最新文献

{"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}

{"title":"Design and time-domain finite element analysis of a carpet thermal concentrator in metamaterials","authors":"Bin He ,&nbsp;Shouzhu Bao","doi":"10.1016/j.camwa.2025.03.016","DOIUrl":"10.1016/j.camwa.2025.03.016","url":null,"abstract":"<div><div>Traditional transform thermodynamic devices are designed from anisotropic materials which are difficult to fabricate. In this paper, we design and simulate a carpet thermal concentrator. Based on existing transformation thermodynamic techniques, we have derived the perfect parameters required for carpet heat concentrators. In order to eliminate the anisotropy of perfect parameters, we designed a heat concentration device for isotropic materials using the effective medium theory, and a posterior error analysis of the finite element discretization scheme in the metamaterial region is provided. Finally, we present the numerical simulation results to verify the correctness of the analysis and the performance of the designed heat concentration device.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"185 ","pages":"Pages 94-109"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696089","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":"Fully consistent lowest-order finite element methods for generalised Stokes flows with variable viscosity","authors":"Felipe Galarce ,&nbsp;Douglas R.Q. Pacheco","doi":"10.1016/j.camwa.2025.03.013","DOIUrl":"10.1016/j.camwa.2025.03.013","url":null,"abstract":"<div><div>In finite element methods for incompressible flows, the most popular approach to allow equal-order velocity-pressure pairs are residual-based stabilisations. When using first-order elements, however, the viscous part of the residual cannot be approximated, which often degrades accuracy. For constant viscosity, or by assuming a Lipschitz condition on the viscosity field, we can construct stabilisation methods that fully approximate the residual, regardless of the polynomial order of the finite element spaces. This work analyses and tests two variants of such a fully consistent approach, with the generalised Stokes system as a model problem. We prove unique solvability and derive expressions for the stabilisation parameter, generalising some classical results for constant viscosity. Numerical results illustrate how our method completely eliminates the spurious pressure boundary layers typically induced by low-order PSPG-like stabilisations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 40-49"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687660","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":"A lattice-Boltzmann inspired finite volume solver for compressible flows","authors":"Jinhua Lu,&nbsp;Song Zhao,&nbsp;Pierre Boivin","doi":"10.1016/j.camwa.2025.03.007","DOIUrl":"10.1016/j.camwa.2025.03.007","url":null,"abstract":"<div><div>The lattice Boltzmann method (LBM) for compressible flow is characterized by good numerical stability and low dissipation, while the conventional finite volume solvers have intrinsic conversation and flexibility in using unstructured meshes for complex geometries. This paper proposes a strategy to combine the advantages of the two kinds of solvers by designing a finite volume solver to mimic the LBM algorithm. It assumes an ideal LBM that can recover all desired higher-order moments. Time-discretized moment equations with second-order temporal accuracy and physically consistent dissipation terms are derived from the ideal LBM. By solving the recovered moment equations, a finite volume solver that can be applied to nonuniform meshes naturally, enabling body-fitted mass-conserving simulations, is proposed. Numerical tests show that the proposed solver can achieve good numerical stability from subsonic to hypersonic flows, and low dissipation for a long-distance entropy spot convection. For the challenging direct simulations of acoustic waves, its dissipation can be significantly reduced compared with the Lax-Wendroff solver of the same second-order spatial and temporal accuracy, while only remaining higher than that of the LBM on coarse meshes. The analysis implies that approximations of third-order temporal accuracy are required to recover the low dissipation of LBM further.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 50-71"},"PeriodicalIF":2.9,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666522","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 decoupled, convergent and fully linear algorithm for the Landau–Lifshitz–Gilbert equation with magnetoelastic effects","authors":"Hywel Normington ,&nbsp;Michele Ruggeri","doi":"10.1016/j.camwa.2025.03.008","DOIUrl":"10.1016/j.camwa.2025.03.008","url":null,"abstract":"<div><div>We consider the coupled system of the Landau–Lifshitz–Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For this nonlinear system of time-dependent partial differential equations, we present a decoupled integrator based on first-order finite elements in space and an implicit one-step method in time. We prove unconditional convergence of the sequence of discrete approximations towards a weak solution of the system as the mesh size and the time-step size go to zero. Compared to previous numerical works on this problem, for our method, we prove a discrete energy law that mimics that of the continuous problem and, passing to the limit, yields an energy inequality satisfied by weak solutions. Moreover, our method does not employ a nodal projection to impose the unit length constraint on the discrete magnetisation, so that the stability of the method does not require weakly acute meshes. Furthermore, our integrator and its analysis hold for a more general setting, including body forces and traction, as well as a more general representation of the magnetostrain. Numerical experiments underpin the theory and showcase the applicability of the scheme for the simulation of the dynamical processes involving magnetoelastic materials at submicrometer length scales.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 1-29"},"PeriodicalIF":2.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666523","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":"Spatiotemporal numerical simulation of breast cancer tumors in one-dimensional nonlinear moving boundary models via temporal-spatial spectral collocation method","authors":"Yin Yang ,&nbsp;Sayyed Ehsan Monabbati ,&nbsp;Emran Tohidi ,&nbsp;Atena Pasban","doi":"10.1016/j.camwa.2025.03.006","DOIUrl":"10.1016/j.camwa.2025.03.006","url":null,"abstract":"<div><div>In this research article, we have simulated the solutions of three types of (classical) moving boundary models in ductal carcinoma in situ by an efficient temporal-spatial spectral collocation method. In all of these three classical models, the associated fixed (spatial) boundary equations are localized by the numerical scheme. In the numerical scheme, Laguerre polynomials and Hermite polynomials are implemented to approximate the temporal and spatial variables (of unknown solutions), respectively. Then, as a generalization of the first classical model, we have considered a space-fractional moving boundary model and then transformed it, again, to the corresponding fixed boundary space-fractional equation for a straightforward discretization. Due to the impossibility of transforming of the time-fractional moving boundary model into its fixed boundary variant, we localized the time-fractional moving boundary model directly by the proposed method. The results in this category are also very satisfactory and the accuracy is again in a spectral rate. Moreover, (temporal) multi-step version of our method is applied for the considered models and the results are very accurate with respect to the single-step one, especially when the boundary of tumor is diverging in practice. In this regard, an adaptive strategy is connected to the temporal multi-step approach for a better simulation. Extensive test problems are provided to verify the accuracy of the method, with full consideration given to iterative tools for solving the final system of nonlinear algebraic equations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 30-49"},"PeriodicalIF":2.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666524","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":"Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations","authors":"Gabriel N. Gatica ,&nbsp;Cristian Inzunza ,&nbsp;Ricardo Ruiz-Baier","doi":"10.1016/j.camwa.2025.03.004","DOIUrl":"10.1016/j.camwa.2025.03.004","url":null,"abstract":"<div><div>We propose mixed finite element methods for the coupled Biot poroelasticity and Poisson–Nernst–Planck equations (modeling ion transport in deformable porous media). For the poroelasticity, we consider a primal-mixed, four-field formulation in terms of the solid displacement, the fluid pressure, the Darcy flux, and the total pressure. In turn, the Poisson–Nernst–Planck equations are formulated in terms of the electrostatic potential, the electric field, the ionized particle concentrations, their gradients, and the total ionic fluxes. The weak formulation, posed in Banach spaces, exhibits the structure of a perturbed block-diagonal operator consisting of perturbed and generalized saddle-point problems for the Biot equations, a generalized saddle-point system for the Poisson equations, and a perturbed twofold saddle-point problem for the Nernst–Planck equations. One of the main novelties here is the well-posedness analysis, hinging on the Banach fixed-point theorem along with small data assumptions, the Babuška–Brezzi theory in Banach spaces, and a slight variant of recent abstract results for perturbed saddle-point problems, again in Banach spaces. The associated Galerkin scheme is addressed similarly, employing the Banach fixed-point theorem to yield discrete well-posedness. A priori error estimates are derived, and simple numerical examples validate the theoretical error bounds, and illustrate the performance of the proposed schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 53-83"},"PeriodicalIF":2.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600613","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":"Multi-material topology optimization of thermoelastic structures by an ordered SIMP-based phase field model","authors":"Minh Ngoc Nguyen ,&nbsp;Nhon Nguyen-Thanh ,&nbsp;Shunhua Chen ,&nbsp;Tinh Quoc Bui","doi":"10.1016/j.camwa.2025.03.005","DOIUrl":"10.1016/j.camwa.2025.03.005","url":null,"abstract":"<div><div>This paper presents a phase field approach to multi-material topology optimization of thermo-elastic structures. Based on the ordered Solid Isotropic Material with Penalization (ordered SIMP) model, the phase field variable is interpreted as the normalized density, which is used as the design variable in topology optimization. The material properties are interpolated in each interval of the normalized density. The advantage of ordered SIMP is that the number of design variables does not depend on the number of materials. In the proposed method, phase field evolution is governed by one Allen-Cahn type equation, with the introduction of a multiple-well potential function to take into account multiple material phases. This feature makes the current approach different from previous works, where numerous phase field evolution equations are needed. In contrast to the original ordered SIMP model, which was developed for structures subjected to only mechanical load, the current approach incorporates interpolation schemes to account for both thermal conductivity and thermal stress coefficient. An assessment of the feasibility and performance of the developed method is conducted via various benchmark examples and comparison with available reference results in the literature.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 84-100"},"PeriodicalIF":2.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600614","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}