In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results...
A balance between model complexity, accuracy, and computational cost is a central concern in numerical simulations. In particular, for stochastic fiber networks, the non-affine deformation of fibers, related non-linear geometric features due to large...
This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this ap...
We report on numerical simulations of a swirling water jet flowing out of a nozzle into a still air atmosphere at normal conditions. Primary jet breakup and atomization were studied with an emphasis on the effect of grid resolution on the results. Je...
The paper introduces a new two-level time-mesh difference scheme for solving the symmetric regularized long wave equation. The scheme consists of three steps. A coarse time-mesh and a fine time-mesh are defined, and the equation is solved using an ex...
As computational fluid dynamics (CFD) has become more mainstream in production engineering workflows, new demands have been introduced that require high-quality meshes to accurately capture the complex geometries. This evolution has created the need...
Low-overhead, robust, and fast-convergent time synchronization is important for resource-constrained large-scale industrial wireless sensor networks (IWSNs). The consensus-based time synchronization method with strong robustness has been paid more at...
This article aims at the development and analysis of a numerical scheme for solving a singularly perturbed parabolic system of n reaction–diffusion equations where m of the equations (with
Unstructured hex meshes are partitions of three spaces into boxes that can include irregular edges, where
In this article, we present an efficient numerical strategy for the two-dimensional nonlinear Schrödinger equation, focusing on its development and analysis. Our approach begins with proposing a nonlinear, energy-conservative, fourth-order, comp...
This paper presents a robust fitted mesh finite difference method for solving a system of n singularly perturbed two parameter convection–reaction–diffusion delay differential equations defined on the interval
This paper presents a robust fitted mesh finite difference method for solving a dynamical system of two parameter convection–reaction–diffusion delay differential equations defined on the interval
This paper proposes a robust finite difference method on a fitted Shishkin mesh to solve a system of n singularly perturbed convection–reaction–diffusion differential equations with two small parameters. Defined on the interval
In this paper, based on the
This article presents a study on singularly perturbed 1D parabolic Dirichlet’s type differential equations with discontinuous source terms on an interior line. The time derivative is discretized using the Euler backward method, followed by the...
The symmetric regularized long wave (SRLW) equation is a mathematical model used in many areas of physics; the solution of the SRLW equation can accurately describe the behavior of long waves in shallow water. To approximate the solutions of the equa...
The finite element method (FEM) is widely used in many engineering applications. The popularity of FEM led to the development of several variants of formulations, and hexahedral meshes surged as one of the most computationally effective. After briefl...
Nonlinear finite element (FE) analysis of reinforced concrete (RC) structures is characterized by numerous modeling options and input parameters. To accurately model the nonlinear RC behavior involving concrete cracking in tension and crushing in com...
The problem of constructing and justifying the discrete algorithms of the support operator method for numerical modeling of differential repeated rotational operations of vector analysis (
Numerical solutions to the adjoint Euler equations have been found to diverge with mesh refinement near walls for a variety of flow conditions and geometry configurations. The issue is reviewed, and an explanation is provided by comparing a numerical...
We present a novel meshing and simulation approach for wind farms, featuring realignment and mesh adaptation. The turbines are modeled with actuator discs, which are discretized by means of an adaptation process to represent a level set function. The...
At present, software products for numerical simulation of fluid dynamics problems (ANSYS Fluent, Ansys CFX, Star CCM, Comsol, etc.) problems are widely used. These software products are mainly based on the numerical solution of the Navier–Stoke...
Lattice structure topology is a rapidly growing area of research facilitated by developments in additive manufacturing. These low-density structures are particularly promising for their medical applications. However, predicting their performance beco...
The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which mu...
This paper aims to numerically study the time-fractional Allen-Cahn equation, where the time-fractional derivative is in the sense of Caputo with order
It is common practice in science and engineering to approximate smooth surfaces and their geometric properties by using triangle meshes with vertices on the surface. Here, we study the approximation of the Gaussian curvature through the Gauss–Bonnet...
A crucial step in any computational fluid dynamics (CFD) analysis is the discretization of the domain because it influences truncation errors, numerical stability, and the convergence of the model. Therefore, the appropriate selection of numerical me...
In this article, a Space-Time Finite Element Method (STFEM) is proposed for the resolution of mechanical problems involving three dimensions in space and one in time. Special attention will be paid to the non-separation of the space and time variable...
Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to bou...
The finite element error and adaptive analysis are implemented in finite element procedures to increase the reliability of numerical analyses. In this paper, the mesh-free error-recovery technique based on moving least squares (MLS) interpolation is...
In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order
We analyse the local discontinuous Galerkin (LDG) method for two-dimensional singularly perturbed reaction–diffusion problems. A class of layer-adapted meshes, including Shishkin- and Bakhvalov-type meshes, is discussed within a general framewo...
This work aims to provide approximate solutions for singularly perturbed problems with periodic boundary conditions using quintic B-splines and collocation. The well-known Shishkin mesh strategy is applied for mesh construction. Convergence analysis...
Due to the strong nonlinearity in the reentry trajectory planning problem for reusable launch vehicles (RLVs), the scale of the problem after high-precision discretization can become significantly large, and the non-convex path constraints are prone...
The
Determining the water table shape and position in unconfined aquifers is fundamental to many groundwater flow assessment studies. The commonly used industry-standard fixed mesh models, contrary to popular belief, do not provide an accurate descriptio...
A moving meshing algorithm with mesh adaptive size function was proposed in this paper with regard to the modeling speed and solution accuracy of electromagnetic equipment in the optimization design process. In the proposed method, a mesh size functi...
In numerical modeling, mesh quality is one of the decisive factors that strongly affects the accuracy of calculations and the convergence of iterations. To improve mesh quality, the Laplacian mesh smoothing method, which repositions nodes to the bary...
This study investigates mesh sensitivity in the buckling analysis of composite cylindrical shells using the finite element methods. Two Carbon Fiber-Reinforced Plastic (CFRP) models with distinct layups were subjected to linear (Eigenvalue) and non-l...
A weak singularity in the solution of time-fractional differential equations can degrade the accuracy of numerical methods when employing a uniform mesh, especially with schemes involving the Caputo derivative (order
Although the grid convergence index is a widely used for the estimation of discretization error in computational fluid dynamics, it still has some problems. These problems are mainly rooted in the usage of the order of a convergence variable within t...
This paper develops a fully discrete finite element scheme for the fractional wave equation with order
Variational mesh refinement is a crucial step in multiview 3D reconstruction. Existing algorithms either focus on recovering mesh details or focus on suppressing noise. Approaches with consideration of both are lacking. To address this limitation, we...
In this paper, we introduce an Adams-type predictor–corrector method based on a modified graded mesh for solving Caputo fractional differential equations. This method not only effectively handles the weak singularity near the initial point but...
A power flow method based on graph theory is presented for three-phase balanced distribution systems. The graph theory is used to describe the power network and facilitate the derivation of the relationship between bus Currents and the bus Voltage Bi...
A newly developed coastal model, FESOM-C, based on three-dimensional unstructured meshes and finite volume, is applied to simulate the dynamics of the southeastern North Sea. Variable horizontal resolution enables coarse meshes in the open sea with r...
Singularly perturbed integro-partial differential equations with reaction–diffusion behavior present significant challenges due to boundary layers arising from small perturbation parameters, which complicate the development of accu...
Supersonic impinging jets are a versatile configuration that can model the compressible flows of cold-spray manufacturing and vertical take-off-and landing strategy. In this work, rhoCentralFoam, solver of the OpenFOAM framework, and a large-eddy sim...
This paper presents a uniformly convergent cubic spline numerical method for a singularly perturbed two-perturbation parameter ordinary differential equation. The considered differential equation is discretized using the cubic spline numerical method...
The emissions from the industrial furnaces impact the environment. Among the various factories, those having anode baking furnaces are working on reducing the pollutant emissions. The aerodynamics in the furnace influences the emissions due to the hi...
of 8