Computers & Mathematics with Applications最新文献

{"title":"A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants","authors":"Yan Ba ,&nbsp;Haihu Liu ,&nbsp;Wenqiang Li ,&nbsp;Wenjing Yang","doi":"10.1016/j.camwa.2024.09.022","DOIUrl":"10.1016/j.camwa.2024.09.022","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327241","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":"Optimized five-by-five block preconditioning for efficient GMRES convergence in curvature-based image deblurring","authors":"Shahbaz Ahmad","doi":"10.1016/j.camwa.2024.09.026","DOIUrl":"10.1016/j.camwa.2024.09.026","url":null,"abstract":"<div><div>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 <span><span>https://github.com/shahbaz1982/Preconditioning</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326369","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":"The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model","authors":"Xiaojing Xu ,&nbsp;Wenjun Sun ,&nbsp;Qi Li","doi":"10.1016/j.camwa.2024.09.021","DOIUrl":"10.1016/j.camwa.2024.09.021","url":null,"abstract":"<div><div>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 <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323875","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":"Robust boundary integral equations for the solution of elastic scattering problems via Helmholtz decompositions","authors":"Víctor Domínguez ,&nbsp;Catalin Turc","doi":"10.1016/j.camwa.2024.09.013","DOIUrl":"10.1016/j.camwa.2024.09.013","url":null,"abstract":"<div><div>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) <span><span>[20]</span></span>). 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) <span><span>[6]</span></span> 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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323861","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 mixed virtual element method for the two-dimensional Navier-Stokes equations in stream-function formulation","authors":"Xi Zhang ,&nbsp;Minfu Feng","doi":"10.1016/j.camwa.2024.09.020","DOIUrl":"10.1016/j.camwa.2024.09.020","url":null,"abstract":"<div><div>This work presents the formulation and analysis of a <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> 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 <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> conforming VEM spaces for both stream function and vorticity and circumventing stringent <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> 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, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> norm for the stream function and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo></math></span> 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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315169","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 hybrid model for accurate prediction of composite longitudinal elastic modulus","authors":"Ilige S. Hage","doi":"10.1016/j.camwa.2024.09.019","DOIUrl":"10.1016/j.camwa.2024.09.019","url":null,"abstract":"<div><div>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.</div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314493","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":"Mathematical modeling and numerical multigoal-oriented a posteriori error control and adaptivity for a stationary, nonlinear, coupled flow temperature model with temperature dependent density","authors":"S. Beuchler ,&nbsp;A. Demircan ,&nbsp;B. Endtmayer ,&nbsp;U. Morgner ,&nbsp;T. Wick","doi":"10.1016/j.camwa.2024.09.017","DOIUrl":"10.1016/j.camwa.2024.09.017","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0898122124004243/pdfft?md5=f79cbd620082379fd38b9188c529a3da&pid=1-s2.0-S0898122124004243-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315170","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 mixed immersed finite element method for fourth-order interface problems on surfaces","authors":"Jiaqi Chen,&nbsp;Xufeng Xiao,&nbsp;Xinlong Feng","doi":"10.1016/j.camwa.2024.09.012","DOIUrl":"10.1016/j.camwa.2024.09.012","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314479","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 stabilizer-free weak Galerkin mixed finite element method for the biharmonic equation","authors":"Shanshan Gu,&nbsp;Fuchang Huo,&nbsp;Shicheng Liu","doi":"10.1016/j.camwa.2024.09.011","DOIUrl":"10.1016/j.camwa.2024.09.011","url":null,"abstract":"<div><div>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 <em>k</em>-th order polynomials, we derive the <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></math></span> convergence rate for the exact solution <em>u</em> in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm and the <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> convergence rate in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. Finally, numerical examples support the results reached by the theory.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314478","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":"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","authors":"Sayahdin Alfat","doi":"10.1016/j.camwa.2024.09.016","DOIUrl":"10.1016/j.camwa.2024.09.016","url":null,"abstract":"<div><div>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 <em>z</em>. 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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311038","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}