Article
Engineering, Multidisciplinary
Cheng-Yu Ku, Chih-Yu Liu, Wei-Po Huang, Jing-En Xiao
Summary: This study presents a meshless method using radial basis function to solve unsaturated flow in heterogeneous porous media, successfully simulating hydrological processes in layered heterogeneous soils. The results demonstrate that this method can enhance the applicability for solving unsaturated flow problems.
JOURNAL OF MARINE SCIENCE AND TECHNOLOGY-TAIWAN
(2021)
Article
Environmental Sciences
Cheng-Yu Ku, Chih-Yu Liu, Frank T-C Tsai
Summary: In this article, a novel approach based on the radial basis function (RBF) method is presented for modeling infiltration-induced landslides in unsaturated soils. The RBF method is used to accurately estimate the relationship between volumetric water content and matric suction, and the meshless method with the RBF is applied to solve the nonlinear Richards equation. The stability of landslides is found to be highly affected by matric potential in unsaturated soils during the infiltration process.
Article
Mathematics, Applied
HongGuang Sun, Yi Xu, Ji Lin, Yuhui Zhang
Summary: A meshless numerical scheme, STBSM, is proposed for solving 3D unsteady advection-diffusion equations using space-time backward substitution method and space-time radial basis function (STRBF). The method introduces compactly supported space-time radial basis function (CS-STRBF) to improve computational efficiency and reduce matrix condition number.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics
Sergey I. Fomenko, Raghavendra B. Jana, Mikhail V. Golub
Summary: This study proposes an advanced mathematical and numerical coupled model to investigate the propagation of elastic waves in multi-layered soils subjected to subsoil water infiltration. The model considers the heterogeneity of the soil and describes the permeability using an inhomogeneous functionally graded fluid-saturation based on Richards' equation. The time-harmonic solution is formulated using the Fourier transform of Green's matrix and the surface load. The study demonstrates the convergence and efficiency of the proposed approach and provides an example of dispersion curves for partially saturated porous strata.
Article
Computer Science, Interdisciplinary Applications
Cheng-Yu Ku, Li-Dan Hong, Chih-Yu Liu, Jing-En Xiao
Summary: This paper proposes a novel meshless approach using space-time polyharmonic radial polynomial basis functions to model saturated and unsaturated flows in porous media. By investigating saturated and unsaturated flow problems, the robustness and high accuracy of the proposed method are demonstrated. The proposed space-time polyharmonic radial polynomial basis functions provide highly accurate solutions and higher accuracy and stability compared to conventional time-marching schemes in solving saturated and unsaturated flow problems.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Kiera van der Sande, Natasha Flyer, Bengt Fornberg
Summary: The use of ML for solving PDEs is a growing research area. In this work, ML is applied to accelerate the RBF-TD method, a numerical discretization scheme for PDEs. The costly L1 minimization step in the original RBF-TD method is replaced with an ERT model, resulting in significant speed up while maintaining high order accuracy.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Water Resources
Nicolae Suciu, Florin A. Radu, Iuliu S. Pop
Summary: Reactive transport in porous media can be upscaled to a larger scale by using coarse-grained space-time (CGST) averages. This approach allows us to model the flow velocity and diffusion coefficient in terms of averaged microscopic quantities, which are verified using global random walk (GRW) simulations. The upscaled approach is applied to biodegradation processes in aquifers and soils, showing significant differences with classical volume averages in time-dependent processes.
ADVANCES IN WATER RESOURCES
(2023)
Article
Mathematics
Lin-Tian Luh
Summary: In this paper, we propose an easily accessible approach to solving differential equations using a choice theory of shape parameters. Our approach is characterized by its high accuracy and efficiency in predicting optimal shape parameter values and achieving extremely small approximation errors in numerical solutions.
Article
Engineering, Multidisciplinary
Fuzhang Wang, Enran Hou, Imtiaz Ahmad, Hijaz Ahmad, Yan Gu
Summary: This paper presents numerical solutions of the second-order one-dimensional hyperbolic telegraph equations using radial basis functions. The purpose is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations by treating the time variable as a normal space variable. The proposed shifted domain method can avoid the full-coefficient interpolation matrix easily, enhancing the numerical solution accuracy.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2021)
Article
Mathematics, Applied
Marzieh Raei, Salvatore Cuomo
Summary: This paper discusses an efficient localized meshless method based on space-time Gaussian radial basis functions for dealing with wave and damped wave equations in high-dimensional space. The method utilizes sparse coefficient matrix, reducing computational costs for high-dimensional problems. Experimental results show computational capabilities and advantages of the presented algorithm.
Article
Computer Science, Interdisciplinary Applications
Dawid Strzelczyk, Maciej Matyka
Summary: In this study, the numerical convergence of the Meshless Lattice Boltzmann Method (MLBM) is investigated through three benchmark tests. The results are compared to the standard Lattice Boltzmann Method (LBM) and the analytical solution of the Navier-Stokes equation. It is found that MLBM outperforms LBM in terms of error value for the same number of nodes discretizing the domain.
COMPUTERS & FLUIDS
(2024)
Article
Agronomy
Vsevolod Bohaienko, Mykhailo Romashchenko, Anastasiia Sardak, Anatolii Gladky
Summary: This paper studies the application of mathematical modelling in drip irrigation management to assess measurement accuracy. A novel modelling framework is proposed to automatically detect and correct measurement inaccuracies, which can be implemented in irrigation decision support systems. Experimental results demonstrate the stability and accuracy of this method in different seasons and with varying amounts of initial data.
IRRIGATION SCIENCE
(2023)
Article
Mathematics, Applied
Brody H. H. Foy, Kevin Burrage, Ian Turner
Summary: This study proposes a meshfree numerical scheme based on strong-form finite volume style formulations. The technique uses radial basis functions to interpolate the problem domain and approximate fluxes in a disjoint finite volume scheme, eliminating the reliance on a mesh structure. The method shows potential for applications in porous media modeling and computational fluid dynamics.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Youssef El Seblani, Elyas Shivanian
Summary: This paper introduces an effective technique called MRPHI for solving partial differential equations with Neumann boundary condition by utilizing radial point interpolation and Hermite-type interpolation techniques. The method is tested on various two-dimensional diffusion equations to demonstrate stability across different arbitrary domains over time.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Zhengjie Sun, Shengliang Zhang
Summary: In this paper, a meshless radial basis function method is proposed to solve the conservative Allen-Cahn equation on smooth compact surfaces embedded in R3. The proposed method inherits the mass conservation property and is established on the operator splitting scheme. It approximates the surface Laplace-Beltrami operator iteratively and discretizes the diffusion equation in time using the Euler method. The reaction equation with a nonlinear function is solved analytically. A kernel-based quadrature formula is employed to approximate the Lagrange multiplier for mass conservation. The meshless conservative scheme is explicit and more efficient than narrow band methods.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Multidisciplinary
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
Summary: We propose a new approach to solve the nonlinear Richards equation using the Kirchhoff transformation and localized radial basis function (LRBF) techniques. This method reduces nonlinearity and models unsaturated flow through heterogeneous soils. We introduce special techniques to handle medium heterogeneity and apply the Kirchhoff transformation with the Brooks and Corey model and a power-law relation. The resulting equation is solved using LRBF methods, which are computationally efficient and avoid mesh generation.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Dongliang Ji, Hui Cheng, Hongbao Zhao
Summary: The influence of crystal size on the macroscopic parameters of sandstone samples is studied using a rock model based on the Voronoi tessellated model. It is found that decreasing crystal size results in increased strength and elastic modulus. Strain energy density (SED) is shown to help explain the failure mechanisms of the sandstone samples. A constitutive model that considers the heterogeneity in elastic modulus and rock strength is developed and is in good agreement with experimental results. The study also identifies the triggering of surface damage on slopes by vibration excitation in engineering applications as well as proposes a constitutive model for quantitatively evaluating damage accumulation in mining tunnels.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Francesco Tornabene, Matteo Viscoti, Rossana Dimitri
Summary: This manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials using the Generalized Differential Quadrature (GDQ) method. The displacement field variable follows the Equivalent Single Layer (ESL) approach, and the geometrical description of the structures is distorted by generalized isogeometric blending functions. Through non-uniform discrete computational grid, the fundamental equations derived from the Hamiltonian principle are solved in strong form. Parametric investigations show the influence of material property variation on the modal response of the structures.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Duy-Khuong Ly, Ho-Nam Vu, Chanachai Thongchom, Nguyen-Thoi Trung
Summary: This paper presents a novel numerical approach for nonlinear analysis and smart damping control in laminated functionally graded carbon nanotube reinforced magneto-electro-elastic (FG-CNTMEE) plate structures, taking into account multiple physical fields. The approach employs a multi-physical coupling isogeometric formulation to accurately capture the nonlinear strain-displacement relationship and the magneto-electro-elastic coupling properties. The smart constrained layer damping treatment is applied to achieve nonlinear damped responses. The formulation is transformed into the Laplace domain and converted back to the time domain through inverse techniques for smart control using viscoelastic materials.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xiaoyang Xu, Jie Cheng, Sai Peng, Peng Yu
Summary: In this study, a smoothed particle hydrodynamics (SPH) method is developed to simulate viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. The method is validated by comparing its solutions with those obtained by the finite volume method (FVM). The method is also used to simulate the impact behavior and dynamics of a viscoelastic droplet, and the influences of various parameters are investigated. The results demonstrate the accuracy and capability of the SPH method in describing the rheological properties and surface variation characteristics of viscoelastic fluid flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xueying Zhang, Yangjiong Wu
Summary: This paper proposes a high resolution strategy for the localized method of approximate particular solutions (LMAPS). The strategy aims to improve the accuracy and stability of numerical calculation by selecting upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate, especially for solving the Navier-Stokes equations with high Reynolds number.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Yong-Tong Zheng, Yijun Liu, Xiao-Wei Gao, Yang Yang, Hai-Feng Peng
Summary: Structures with holes are common in engineering applications. Analyzing stress concentration effects caused by holes using FEM or BEM is challenging and time-consuming. This paper proposes improved methods for simulating holes and cylinders, reducing the number of nodes while maintaining stress accuracy. Numerical examples demonstrate the accuracy and efficiency of the proposed methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Chein-Shan Liu, Chung-Lun Kuo
Summary: The paper presents two new families of fundamental solutions for the 3D Laplace equation and proposes the methods of pseudo fundamental solutions and anisotropic fundamental solutions, which outperform the traditional 3D MFS.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Sima Shabani, Miroslaw Majkut, Slawomir Dykas, Krystian Smolka, Esmail Lakzian
Summary: This study validates and simulates steam condensing flows using different condensation models and equations of state, identifying the most suitable model. The results highlight the importance of choosing the appropriate numerical model for accurately predicting steam condensation flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
D. L. Guo, H. H. Zhang, X. L. Ji, S. Y. Han
Summary: In this study, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes were investigated using the numerical manifold method (NMM). The proposed method was verified and found to have good convergence and accuracy. Additionally, the effects of material principal direction and hole configurations on the mechanical behaviors of the orthotropic composites were revealed.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Giacomo Rosilho de Souza, Rolf Krause, Simone Pezzuto
Summary: In this paper, we propose a boundary element method for accurately solving the cell-by-cell bidomain model of electrophysiology. The method removes the degeneracy in the system and reduces the number of degrees of freedom. Numerical experiments demonstrate the exponential convergence of our scheme in space and several biologically relevant experiments are provided.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Riku Toshimitsu, Hiroshi Isakari
Summary: This study extends a recent paper by Lai et al. (2018) by introducing a novel boundary integral formulation for scalar wave scattering analysis in two-dimensional layered and half-spaces. The modified integral formulation eliminates fictitious eigenvalues and reasonable parameter settings ensure efficient and accurate numerical solutions. The proposed method is demonstrated to be effective through numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Ebutalib Celik, Merve Gurbuz-Caldag
Summary: In this paper, a new meshless method based on domain decomposition for an L-shaped domain is proposed, which uses RBF-FD formulation at interface points and classical FD in sub-regions to improve the solution accuracy. The proposed numerical method is applied to simulate benchmark results for a divided-lid driven cavity and solve Navier-Stokes equations with Lorentz force term in a single-lid L-shaped cavity exposed to inclined magnetic field, and the flow structure is analyzed in terms of streamline topology under different magnetic field rotations and strengths.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Hanqing Liu, Fajie Wang, Lin Qiu, Cheng Chi
Summary: This paper presents a novel method that combines the singular boundary method with the Loop subdivision surfaces for acoustic simulation of complex structures, overcoming technical challenges in handling boundary nodes.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)