Computers & Mathematics with Applications最新文献

In this paper, we consider a locking-free numerical method for the poroelasticity-Forchheimer problem, which exists locking phenomenon when directly using the continuous Galerkin mixed finite element method (MFEM) to be solved due to the influence of special physical parameters. To overcome the locking phenomenon, we reformulate the original problem into a new problem by introducing some new variables. The new problem can be taken as a Stokes-diffusion coupled model, which exists a built-in mechanism to circumvent the locking phenomenon for continuous Galerkin MFEM. Moreover, we prove the existence and uniqueness of weak solution with the help of a priori error estimate, some invariant quantities and the discussion on nonlinear term. After that, we propose a fully discrete numerical scheme to solve the reformulated problem, where the DL-scheme and L-scheme are designed to deal with the nonlinear term, and prove the optimal convergence in both time and space. Finally, numerical tests are presented to verify the theoretical results.

We consider time-dependent eddy current problem formulated in terms of the electric field that is discretized by Nédélec finite elements in space and by the backward Euler scheme in time. We derive residual-based a posteriori error estimates in the energy norm augmented by temporal jumps in the numerical solution. The estimates are reliable and locally efficient in both time and space.

This study presents an investigation into the collision dynamics of particulate droplets using a two-dimensional Lattice Boltzmann Method (LBM) framework, enhanced by a phase-field model based on the Allen-Cahn (A-C) equation. The paper validates the LBM approach against established references, ensuring accuracy and reliability. Simulations cover head-on and off-center collisions under various conditions, including different particle sizes and numbers, as well as varying Weber and Reynolds numbers. The findings demonstrate that particles within droplets significantly influence the collision dynamics, particularly in terms of momentum transfer and collision asymmetry. The research highlights the complex interplay between particle dynamics and droplet behavior, offering insights into industrial processes such as pharmaceuticals, coating applications, and the oil and energy sectors. The study contributes to the broader understanding the nuanced effects of particles in droplet collisions and the results and methodologies presented can be applied to various practical applications.

This study introduces an efficient numerical methodology for the analysis of three-dimensional (3D) elastodynamics, featuring high-order precision in the temporal and spatial domains. In the temporal discretization process using the Krylov deferred correction (KDC) technique, the second-order time derivative is treated as a new variable in the governing equations. Spectral integration is then employed to mitigate the instability associated with numerical differentiation operators. Additionally, an improved numerical implementation of boundary conditions based on time integration is incorporated into the KDC approach. The boundary value problems at time nodes resulting from the above discretization process are resolved by employing generalized finite difference method (GFDM), providing the flexibility to choose the Taylor series expansion order. We present four numerical examples to indicate the performance of the developed method in the accuracy and stability. The obtained numerical results are meticulously compared with either analytical solutions or those calculated using COMSOL software.

This work tackles a novel parabolic equation driven by a nonlinear operator with double variable exponents, aiming to decompose and denoise images. Our primary approach involves enhancing classical models based on variable exponent operators by considering a novel nonlinear operator having a double-phase flux with unbalanced growth. We begin initially by analyzing the theoretical solvability of our model. Employing the Musielak-Orlicz space, we establish a suitable functional framework for investigating the proposed model. Subsequently, we use the Faedo-Galerkin approach to establish the existence and uniqueness of a weak solution for our problem. Furthermore, we provide a demonstration showcasing how our model preserves solution positivity, emphasizing this as a consistent feature of the proposed model. To evaluate our theoretical results, we present various numerical simulations on some grayscale and medical images (Magnetic Resonance Images (MRI)). These simulations covered aspects like decomposition, robustness and behavior sensitivity of model parameters with visual and quantitative comparisons. The obtained numerical results strongly support the efficiency of the proposed model in preserving features, reducing artifacts and deleting noise in comparison to some well-known existing state-of-the-art models. Furthermore, the proposed model quantitatively surpasses the competitive models in terms of several well-known criteria, namely the Peak Signal-to-Noise Ratio (PSNR), the Structural Similarity Index (SSIM) and the Mean-Square Error (MSE).

In this paper, we study the bilinear finite volume element method for solving the singularly perturbed convection-diffusion problem on the Shishkin mesh. We first prove that the finite volume element scheme is ϵ-uniformly stable. Then, based on new expression of the finite volume bilinear form and some detailed integral calculations, an ϵ-uniform error estimation is derived in the ϵ-weighted gradient norm, including the $L_2$-norm. This error estimate is better than the known result. Moreover, we also give the $L_{\infty }$-error estimate near the boundary layer regions. At last, numerical experiments show the effectiveness of our method.

Acoustic waves in water pipes pose a structural threat but also offer a valuable tool for non-invasive inspection. Complex pipe geometries such as bends and surface liners create complex fluid boundaries, triggering interactions between fluid flow and acoustics. The lattice Boltzmann method (LBM) excels at capturing these interactions near complex boundaries, in contrast to the finite volume method, which can result in errors. However, the application of LBM in water pipes has been limited by stability problems. This study proposes a two-step (DM-TS) collision operator based on a direct method (LBM-HA) for stable LBM simulations in water pipes. LBM-HA enables direct hydroacoustic predictions for both acoustic and dynamic flow fields in a pipe orifice. A novel acoustic-dynamic complex boundary condition was formulated from the linearized Euler's equation to account for the physical effects of the bounded domain of the LBM-HA analysis. To distinguish between dynamic and acoustic components, wavenumber and frequency decomposition techniques were applied to the pressure data obtained within the pipe. In addition, mode decomposition of the acoustic pressure was conducted to identify the dominant acoustic modes. By comparing the LBM-HA results with experimental data, we highlighted the method's potential for direct hydroacoustic analysis considering the acoustic characteristics of the water pipe.

This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of imposing outflow boundary conditions. The coercivity of the homogeneous least-squares functionals are established, and the a priori error estimates of the least-squares methods are obtained in a norm that incorporates the streamline derivative. All methods have the same convergence rate provided that meshes in the layer regions are fine enough. To increase computational accuracy and reduce computational cost, adaptive least-squares methods are implemented and numerical results are presented for some test problems.

This research paper presents an innovative technique for shadow images removal. The method involves redefining a contemporary osmosis model by incorporating bilateral total variation (TV) operators. This integration allows to take advantage of robust anisotropic diffusion, resulting in improved image restoration. The paper also outlines new mathematical derivation of the bilateral TV and a combination with nonlinear anisotropic transport term. The experimental results substantiate the effectiveness of the anisotropic osmosis model, showcasing its superior qualitative and quantitative performance when compared to current state-of-the-art techniques.

In this paper, a mathematical model of semiconductor device with two important factors is discussed. Heat and magnetic influences are considered together. Its numerical approximation is important in information science and other technological innovation fields. The major physical unknowns (the potential, electron concentration, hole concentration, and the heat) are defined by four nonlinear PDEs: an elliptic equation, two convection-diffusion equations and a heat conductor equation. A conservative block-centered method is used to approximate the elliptic equation. The derivatives to time t, $\frac{\partial }{\partial t}(\cdot )$, are discretized by multistep differences for improving the computational accuracy. The diffusions and convection terms are treated by block-centered differences and upwind approximations, respectively. This composite numerical method is suitable for this nonlinear system. Firstly, numerical dispersion and nonphysical oscillations are avoided. Secondly, the unknowns and their adjoint vectors are obtained simultaneously. Thirdly, the law of conservation is preserved. An error estimates is derived. Finally, simple examples are given for showing the efficiency and accuracy.