Computers & Mathematics with Applications最新文献

Approximate deconvolution and velocity estimation modeling of decaying Burgers turbulence 衰减Burgers湍流的近似反褶积和速度估计模型

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.023

A. Boguslawski , K. Wawrzak , B.J. Geurts

{"title":"Approximate deconvolution and velocity estimation modeling of decaying Burgers turbulence","authors":"A. Boguslawski , K. Wawrzak , B.J. Geurts","doi":"10.1016/j.camwa.2025.06.023","DOIUrl":"10.1016/j.camwa.2025.06.023","url":null,"abstract":"<div><div>The paper presents Burgers turbulence simulated using Large Eddy Simulations (LES). Two types of subfilter models are applied: Approximate Deconvolution Model (ADM) and Velocity Estimation Concept (VEC). In the ADM approach, two different filter types were applied indicating the influence of the filter on the deconvolution convergence via comparison with a direct inversion method. In both approaches the ADM and VEC the deconvolved and estimated fields are shown. It is stressed that ADM introduces flow structures characterized by subfilter scales down to the mesh cut-off length scale. In the case of the VEC only the kinematic step was applied for the subgrid velocity field estimation. We observe that both ADM and VEC provide predictions that are closely related to direct numerical simulations (DNS) provided the spatial resolution is adequate. Moreover, results based on the top-hat filter as the basis for LES are in general agreement with results obtained on the basis of a sixth-order Padé filter. The VEC model provides further opportunities to include much finer scales that evolve under simplified approximate dynamics, thereby enabling additional fine-tuning of the predictions of higher-order statistical quantities.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 279-296"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517051","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}

引用次数: 0

A second-order maximum bound principle-preserving exponential Runge–Kutta scheme for the convective Allen–Cahn equation 对流Allen-Cahn方程的二阶最大界保原理指数Runge-Kutta格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.029

Yan Wang, Haifeng Wang, Hong Zhang, Xu Qian

{"title":"A second-order maximum bound principle-preserving exponential Runge–Kutta scheme for the convective Allen–Cahn equation","authors":"Yan Wang, Haifeng Wang, Hong Zhang, Xu Qian","doi":"10.1016/j.camwa.2025.06.029","DOIUrl":"10.1016/j.camwa.2025.06.029","url":null,"abstract":"<div><div>We present and analyze a time-stepping scheme that is efficient and second-order accurate for the convective Allen–Cahn equation with a general mobility function. By employing the second-order central finite difference discretization for the diffusion term and the upwind discretization for the advection term, we develop a temporally two-stage second-order exponential Runge–Kutta scheme (ERK2) by incorporating a stabilization technique. It is demonstrated that the ERK2 unconditionally satisfies the discrete maximum bound principle (MBP) for both the polynomial Ginzburg–Landau potential and the logarithmic Flory–Huggins potential. Leveraging the uniform boundedness of numerical solutions guaranteed by the MBP, we prove the second-order convergence rate in the discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-norm. Furthermore, we establish the unconditionally energy dissipation property of the ERK2 scheme in the case of a constant mobility. Various numerical experiments corroborate our theoretical findings. Notably, these experiments indicate that the proposed ERK2 scheme not only achieves better computational accuracy but also significantly enhances efficiency compared to the classic second-order exponential time differencing Runge–Kutta (ETDRK2) scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 297-314"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517052","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}

引用次数: 0

Optimal error estimates of a decoupled, linear, unconditionally stable and charge-conservative finite element scheme for a thermally coupled incompressible IMHD system 热耦合不可压缩IMHD系统解耦线性无条件稳定电荷保守有限元格式的最优误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.016

Jinmiao Ren , Xia Cui

{"title":"Optimal error estimates of a decoupled, linear, unconditionally stable and charge-conservative finite element scheme for a thermally coupled incompressible IMHD system","authors":"Jinmiao Ren , Xia Cui","doi":"10.1016/j.camwa.2025.06.016","DOIUrl":"10.1016/j.camwa.2025.06.016","url":null,"abstract":"<div><div>We develop and analyze a decoupled, linear, unconditionally stable, charge-conservative fully discrete scheme for a thermally coupled incompressible inductionless magneto-hydrodynamics (IMHD) system. Due to the nonlinearity and coupling of the system, developing a decoupled and practically effective scheme has always been a challenging problem. We overcome the difficulty by discretizing the temporal variables with the backward Euler method, linearizing the nonlinear convection term and decoupling the velocity, current density and temperature with implicit-explicit (IMEX) techniques, as well as decoupling the velocity and pressure with pressure-projection method. By discretizing the spatial variables with the finite element method, we acquire high accuracy. It is worth noting that the scheme is easy to implement since it requires solving merely a linear subsystem at each time step. Moreover, it is unconditionally stable, and yields an exactly divergence free current density directly. By introducing various finite element projections and developing novel inductive reasoning techniques, we gain optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> error estimates for the velocity, temperature, current density, pressure and electric potential. Numerical tests are provided to verify the good performance of the scheme such as the accuracy and charge conservation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 253-278"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517050","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}

引用次数: 0

A high-order blended compact difference (BCD) scheme for two-dimensional steady incompressible viscous flows 二维定常不可压缩粘性流的高阶混合紧致差分格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.028

Tingfu Ma , Yongbin Ge

引用次数: 0

Error analysis of the moving least square material point method for large deformation problems 大变形问题的移动最小二乘质点法误差分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.030

Huanhuan Ma

引用次数: 0

U-WNO: U-Net enhanced wavelet neural operator for solving parametric partial differential equations U-WNO：用于求解参数偏微分方程的U-Net增强小波神经算子

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-01 DOI: 10.1016/j.camwa.2025.06.024

Wei-Min Lei, Hou-Biao Li

{"title":"U-WNO: U-Net enhanced wavelet neural operator for solving parametric partial differential equations","authors":"Wei-Min Lei, Hou-Biao Li","doi":"10.1016/j.camwa.2025.06.024","DOIUrl":"10.1016/j.camwa.2025.06.024","url":null,"abstract":"<div><div>High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets' time-frequency localization to capture spatial manifolds effectively. While its factorization strategy improves noise robustness, it suffers from high-frequency information loss caused by finite-scale wavelet decomposition. In this study, a new U-WNO network architecture is proposed. It incorporates the U-Net path and residual shortcut into the wavelet layer to enhance the extraction of high-frequency features and improve the learning of spatial manifolds. Furthermore, we introduce an adaptive activation mechanism to mitigate spectral bias through trainable slope parameters. Extensive benchmarks across seven PDE families (Burgers, Darcy flow, Navier-Stokes, etc.) show that U-WNO achieves 45–83% error reduction compared to baseline WNO, with mean <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> relative errors ranging from 0.043% to 1.56%. This architecture establishes a framework combining multiresolution analysis with deep feature learning, addressing the spectral-spatial tradeoff in operator learning. Code and data used are available on <span><span>https://github.com/WeiminLei/U-WNO.git</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 272-287"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517627","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}

引用次数: 0

Higher-order generalized finite differences for variable coefficient diffusion operators 变系数扩散算子的高阶广义有限差分

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-06-27 DOI: 10.1016/j.camwa.2025.06.018

Heinrich Kraus , Jörg Kuhnert , Pratik Suchde

{"title":"Higher-order generalized finite differences for variable coefficient diffusion operators","authors":"Heinrich Kraus , Jörg Kuhnert , Pratik Suchde","doi":"10.1016/j.camwa.2025.06.018","DOIUrl":"10.1016/j.camwa.2025.06.018","url":null,"abstract":"<div><div>We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 257-271"},"PeriodicalIF":2.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144502364","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}

引用次数: 0

H1-norm error analysis of an ADI compact finite difference method for a two-dimensional time-fractional reaction-diffusion equation with variable coefficients 二维变系数时分数阶反应扩散方程ADI紧致有限差分法的h1范数误差分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-06-25 DOI: 10.1016/j.camwa.2025.06.011

P. Roul , S.N. Khandagale , Jianxiong Cao

{"title":"H1-norm error analysis of an ADI compact finite difference method for a two-dimensional time-fractional reaction-diffusion equation with variable coefficients","authors":"P. Roul , S.N. Khandagale , Jianxiong Cao","doi":"10.1016/j.camwa.2025.06.011","DOIUrl":"10.1016/j.camwa.2025.06.011","url":null,"abstract":"<div><div>This paper introduces a robust numerical approach based on an alternating implicit direction (ADI) compact finite difference scheme for approximating the solution of a variable coefficient time fractional reaction-diffusion (TFRD) model in two space dimensions. The model is characterized by initial weak singularity. We apply the L1 formula for discretization of the temporal fractional derivative (TFD) on a graded mesh while the space derivatives are approximated by a high-order ADI compact finite difference scheme. The solvability of this method is investigated. We present a framework for examining stability result and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm global error estimate of the proposed scheme. Numerical experiment is carried out to demonstrate the accuracy of the algorithm and to verify the theoretical results. We compare the computed results on the graded grids with those on the uniform grid to show the advantage of the graded grids method. The present study is the first work on design and analysis of L1-ADI method for the TFRD model with variable coefficients in two dimensions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"194 ","pages":"Pages 135-157"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470409","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}

引用次数: 0

Positivity-preserving DDFV scheme for compressible two-phase flow in porous media 多孔介质中可压缩两相流的保正DDFV格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-06-25 DOI: 10.1016/j.camwa.2025.06.007

Thomas Crozon, El Houssaine Quenjel, Mazen Saad

引用次数: 0

A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation 非线性分数阶Fisher-Kolmogorov方程数值解的局部傅里叶配点法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-06-25 DOI: 10.1016/j.camwa.2025.06.020

Farzaneh Safari , Ji Lin , Yanjun Duan

引用次数: 0