Yuyang Liu^1,2,*, Wensheng Zhou^1,2, Zhijie Wei^1,2, Engao Tang^1,2, Chenyang Shi³, Qirui Zhang^4,*, Zifeng Chen⁴

Energy Engineering, Vol.122, No.10, pp. 4245-4260, 2025, DOI:10.32604/ee.2025.066167 - 30 September 2025

Abstract After a long period of water flooding development, the oilfield has entered the middle and high water cut stage. The physical properties of reservoirs are changed by water erosion, which directly impacts reservoir development. Conventional numerical reservoir simulation methodologies typically employ static assumptions for model construction, presuming invariant reservoir geological parameters throughout the development process while neglecting the reservoir’s temporal evolution characteristics. Although such simplifications reduce computational complexity, they introduce substantial descriptive inaccuracies. Therefore, this paper proposes a meshless numerical simulation method for reservoirs that considers time-varying characteristics. This method avoids the meshing in traditional… More >

Hongwei Ma¹, Yingqian Tian^2,*, Fuzhang Wang^3,*, Quanfu Lou⁴, Lijuan Yu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3419-3432, 2025, DOI:10.32604/cmes.2025.070791 - 30 September 2025

Abstract This study introduces a novel single-layer meshless method, the space-time collocation method based on multiquadric-radial basis functions (MQ-RBF), for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation. By reconstructing the time variable as a space variable, this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods. By introducing shape parameter-optimized MQ-RBF, high-precision discretization of the nonlinear, dispersive, and dissipative terms in the BBMB equation is achieved. The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples. This method shows significant advantages in computational efficiency, More >

Wenna He, Yichen Yang, Dongqiong Liang, Heng Cheng^*

CMC-Computers, Materials & Continua, Vol.83, No.1, pp. 1415-1414, 2025, DOI:10.32604/cmc.2025.059839 - 26 March 2025

Abstract In this paper, we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods. The approximation function is established based on the improved moving least squares (IMLS) method, which enhances the efficiency and stability of the numerical solution. The numerical solution formulas are derived using the improved element-free Galerkin (IEFG) method. We introduce the solid isotropic microstructures with penalization (SIMP) model to formulate a mathematical model for topology optimization, which effectively penalizes intermediate densities. The optimization problem is defined with the numerical solution formula and volume fraction as constraints. The… More >

Mohammad-Rahim Hematiyan^*

CMC-Computers, Materials & Continua, Vol.82, No.2, pp. 3069-3090, 2025, DOI:10.32604/cmc.2025.060067 - 17 February 2025

Abstract The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using inverse methods in which displacement or strain measurements are taken at several points on the body. This paper presents an inverse method based on the method of fundamental solutions for the traction identification problem in two-dimensional anisotropic elasticity. The method of fundamental solutions is an efficient boundary-type meshless method widely used for analyzing various problems. Since the problem is linear, the… More >

Tan Phat Lam^1,2, Chia-Ming Fan^1,*, Chiung-Lin Chu¹, Fu-Li Chang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.32, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012160

Abstract In this study, the combination of the Method of Fundamental Solutions (MFS) and the Particle Swarm Optimization (PSO) is proposed to accurately and stably analyze the multi-dimensional diffusion equations. The MFS, truly free from mesh generation and numerical quadrature, is one of the most promising meshless methods. In the implementation of the MFS, only field points and sources, which are located out of the computational domain, are required. The numerical solutions of the MFS is expressed as a linear combination of diffusion fundamental solutions with different strengths. The unknown coefficients in the solution expressions can… More >

Tsung-Han Li^1,*, Chia-Ming Fan¹, Po-Wei Li²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.32, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012120

Abstract The generalized finite difference method (GFDM), which cooperated with the fictitious-nodes technique, is proposed in this study to accurately analyze three-dimensional boundary value problems, governed by high-order partial differential equations. Some physical applications can be mathematically described by boundary value problems governed by high-order partial differential equations, but it is non-trivial to analyze the high-order partial differential equations by adopting conventional mesh-based numerical schemes, such as finite difference method, the finite element method, etc. In this study, the GFDM, a localized meshless method, is proposed to accurately and efficiently solve boundary value problems governed by… More >

Taku Itoh^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.4, pp. 1-1, 2024, DOI:10.32604/icces.2024.012260

Abstract In meshless methods, although elements constructing an analysis domain are not required, the domain should be represented in some way, instead. A scalar field g(x), that contains the analysis domain, is sometimes employed, and the boundary of analysis domain is represented as an implicit surface, g(x) = 0. In this study, we consider generating an implicit surface from scattered points on the surface of an object. The scattered points are obtained by a three-dimensional scanning device. To generate g(x), field values f_ijk on N3 uniform grid points x_ijk are required. Although the field values f_ijk have been… More >

Junsong Xiong¹, Zhen Wang², Shaofan Li³, Xin Lai^1,*, Lisheng Liu^2,*, Xiang Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 151-169, 2024, DOI:10.32604/cmes.2024.053078 - 20 August 2024

Abstract Natural convection is a heat transfer mechanism driven by temperature or density differences, leading to fluid motion without external influence. It occurs in various natural and engineering phenomena, influencing heat transfer, climate, and fluid mixing in industrial processes. This work aims to use the Updated Lagrangian Particle Hydrodynamics (ULPH) theory to address natural convection problems. The Navier-Stokes equation is discretized using second-order nonlocal differential operators, allowing a direct solution of the Laplace operator for temperature in the energy equation. Various numerical simulations, including cases such as natural convection in square cavities and two concentric cylinders, More >

Chih-Ping Wu^*, Ruei-Syuan Chang

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 917-949, 2024, DOI:10.32604/cmes.2024.052307 - 20 August 2024

Abstract This work develops a Hermitian C differential reproducing kernel interpolation meshless (DRKIM) method within the consistent couple stress theory (CCST) framework to study the three-dimensional (3D) microstructure-dependent static flexural behavior of a functionally graded (FG) microplate subjected to mechanical loads and placed under full simple supports. In the formulation, we select the transverse stress and displacement components and their first- and second-order derivatives as primary variables. Then, we set up the differential reproducing conditions (DRCs) to obtain the shape functions of the Hermitian C differential reproducing kernel (DRK) interpolant’s derivatives without using direct differentiation. The interpolant’s… More >

Xin Liu^1,*, Kai Yan², Bo Fang³, Xiaoyu Sun³, Daqiang Feng⁴, Li Yin⁵

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.7, pp. 1539-1552, 2024, DOI:10.32604/fdmp.2024.047922 - 23 July 2024

Abstract In response to the complex characteristics of actual low-permeability tight reservoirs, this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs, considering complex boundary shapes. Utilizing radial basis function point interpolation, the method approximates shape functions for unknown functions within the nodal influence domain. The shape functions constructed by the aforementioned meshless interpolation method have δ-function properties, which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells. Moreover, the meshless method offers greater flexibility and freedom compared to grid cell discretization, making it simpler… More >