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radial basis function method for Predicting the Evolution of Aerosol Size Distributions for Coagulation Problems

ATMOSPHERE 2022年第11期13卷 1895-1895页

作者： Wang, Kaiyuan Hu, Run Xiong, Yuming Xie, Fei Yu, Suyuan Huazhong Univ Sci & Technol Sch Energy & Power Engn Wuhan 430074 Peoples R China Smoore Int Holdings Ltd Shenzhen 518102 Peoples R China Tsinghua Univ Dept Energy & Power Engn Beijing 100084 Peoples R China

The dynamic evolution of particle size distributions (PSDs) during coagulation is of great importance in many atmospheric and engineering applications. To date, various numerical methods have been developed for solving the general dynamic equation under different scenarios. In this study, a radial basis function (RBF) method was proposed to solve particle coagulation evolution. This method uses a Gaussian function as the basis function to approximate the size distribution function. The original governing equation was then converted to ordinary differential equations (ODEs), along with numerical quadratures. The RBF method was compared with the analytical solutions and sectional method to validate its accuracy. The comparison results showed that the RBF method provided almost accurate predictions of the PSDs for different coagulation kernels. This method was also verified to be reliable in predicting the self-preserving distributions reached over long periods and for describing the temporal evolution of moments. For multimodal coagulation, the RBF method also accurately predicted the temporal evolution of a bimodal distribution owing to scavenging effects. Moreover, the computational times of the RBF method for these cases were usually of the order of seconds. Thus, the RBF method is verified as a reliable and efficient tool for predicting PSD evolution during coagulation.

关键词： radial basis function method particle size distribution population balance coagulation

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Analytical assessment of the time-space fractional bioheat transfer equation by the radial basis function method for living tissues

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HEAT TRANSFER 2022年第7期51卷 6139-6161页

作者： Hosseinzadeh, Saman Mousavi, Seyed M. Emadi, Seyed M. Ganji, Davood D. Babol Noshirvani Univ Technol Dept Mech Engn Babol Iran

In recent years, thermal treatment has proven to be helpful, notably in oncology. In fact, ablating the superfluous mass and eliminating the malignant tumor using a different modality such as warmth or cooling is a therapeutic method. In this study, the radial basis function approach was used to answer the time-space fractional heat transfer equations of human body tissue during thermal therapy. To validate the radial basis function technique, it was also compared to the fourth-order Runge-Kutta numerical method. The findings demonstrated that this methodology is extremely accurate and efficient, with an error rate of less than 1%. The effect of time and spatial fractional parameters, blood perfusion coefficient, metabolic coefficient, and internal source coefficient on the temperature profile inside human living tissues has been studied and depicted well.

关键词： fractional bioheat equations human living tissues radial basis function method thermal therapy

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Mathematical modeling of fractional derivatives for magnetohydrodynamic fluid flow between two parallel plates by the radial basis function method

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Theoretical & Applied Mechanics Letters 2022年第4期12卷 241-250页

作者： Saman Hosseinzadeh Seyed Mahdi Emadi Seyed Mostafa Mousavi Davood Domairry Ganji Department of Mechanical Engineering Babol Noshirvani University of TechnologyBabolIran

Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years,owing to their practical significance and numerous applications in astro-physical and geo-physical *** this paper,the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic *** magnetohydrodynamics coupled stress fluid flows between two parallel plates,with the bottom plate being stationary and the top plate moving at a persistent *** compared the radial basis function approach to the numerical method(fourth-order Range-Kutta)in order to verify its *** findings demonstrated that the discrepancy between these two techniques is quite negligible,indicating that this method is very *** impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is ***,the velocity parameter is compared for diverse conditionsα,Reynolds and position(y),the maximum of which occurs atα=***,the maximum velocity values occur inα=0.4 and Re=1000 and the concavity of the graph is less forα=0.8.

关键词： Magnetohydrodynamic fluid Fractional equation radial basis function method Numerical method

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Laminar Rayleigh-Benard convection in a closed square field with meshless radial basis function method

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CURVED AND LAYERED STRUCTURES 2023年第1期10卷

作者： Santosa, Irfan Budiana, Eko Prasetya Hadi, Syamsul Wijayanta, Agung Tri Univ Sebelas Maret Fac Engn Dept Mech Engn Jalan Ir Sutami 36A Surakarta 57126 Indonesia

Research on natural convection is exciting in some experimental and numerical cases, especially in rectangular cavities with relatively low heat dissipation and thermal control systems with low cost, reliability, and ease of use. The present study will use the meshless radial basis function method to solve the velocity formulation of the Navier-Stokes equations by varying some nominal Rayleigh numbers of 10(4), 10(5), and 10(6). The numerical accuracy is compared with the previous research. The advantages of the meshless method are that it does not require a structured mesh and does not require inter-nodal connectivity. The results show that the temperature pattern is identical to the previous research. The calculations have been done for three different Rayleigh numbers of 10(4), 10(5), and 10(6) for 151 x 151 nodes. The variations of the Ra number will affect the isothermal, velocity contours, and Nusselt number.

关键词： laminar convection Rayleigh-Benard radial basis function method

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Assessment of radial basis function Network method for Fractal-Like Agglomerate Dynamics

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AEROSOL SCIENCE AND ENGINEERING 2024年第3期8卷 307-318页

作者： Ma, Chang Yu, Mingzhou China Jiliang Univ Lab Aerosol Sci & Technol Xueyuan St 258 Hangzhou 310018 Zhejiang Peoples R China

During physical and chemical processes, aerosol particles often undergo coagulation to form Agglomerates. Agglomerates are fractal-like in a statistical sense, whose dynamical evolution of particle size distribution is governed by the population balance equation (PBE). In this study, the radial basis function (RBF) method RBF is firstly extended to the solution of fractal-like agglomerate dynamics problems. The applicable conditions, and advantages and disadvantages of this method are studied. Two dynamic processes of fractal-like agglomerates, namely Brownian coagulation in the continuum regime and Brownian coagulation in the free molecular regime, are investigated. As a comparison, the sectional method (SM) is utilized as the referenced method. The initial geometric standard deviation (GSD) and the fractal dimension (D-f) of agglomerates are found to be the two main key factors affecting the accuracy and efficiency of the RBF. The RBF method is more suitable for calculating cases with larger GSD. As the GSD increases (i.e., GSD > 1.2), the computational efficiency and accuracy of the RBF increase accordingly. The RBF method is more suitable for calculating cases with larger D-f . As the D-f decreases, the calculation error of RBF method becomes further larger, which is more obvious in the free molecular regime. Compared with the SM method, the calculation efficiency of RBF method increases by 3-4 orders of magnitude. This study provides excellent application of RBF method to the solution of the PBE.

关键词： radial basis function method Population balance equation Fractal-like agglomerate dynamics Brownian coagulation

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A Reduced radial basis function method for Partial Differential Equations on Irregular Domains

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JOURNAL OF SCIENTIFIC COMPUTING 2016年第1期66卷 67-90页

作者： Chen, Yanlai Gottlieb, Sigal Heryudono, Alfa Narayan, Akil Univ Massachusetts Dartmouth Dept Math N Dartmouth MA 02747 USA

We propose and test the first Reduced radial basis function method for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable radial basis function (RBF) solver that has an optimized set of centers chosen through a reduced-basis-type greedy algorithm, and a collocation-based model reduction approach that systematically generates a reduced-order approximation whose dimension is orders of magnitude smaller than the total number of RBF centers. The resulting algorithm is efficient and accurate as demonstrated through two- and three-dimensional test problems.

关键词： Reduced basis method radial basis function method Pseudospectral method Model reduction

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A novel approach for assessment of MHD mixed fluid around two parallel plates by consideration hybrid nanoparticles and shape factor

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ALEXANDRIA ENGINEERING JOURNAL 2022年第12期61卷 9779-9793页

作者： Hosseinzadeh, Saman Ganji, Davood Domiri Babol Noshirvani Univ Technol Dept Mech Engn Babol Iran

In the presence of a uniform magnetic field, the heat and mass transmission mechanisms of steady magnetohydrodynamic nanofluid flows between two parallel plates are presented in this paper. Ethylene glycol and water are mixed in equal proportions in the fluid. The hybrid nanoparticle is analyzed in this work, utilizing MWCNT and Ag as the particles. As a novelty, the nonlinear equations were solved using the radial basis function methodology for the first time, and the numerical fourth-order Runge-Kutta method was used to compare the results, which were then illustrated in figures. The end result demonstrates that the numerical method and the radial basis function approach are in excellent accord. Furthermore, the impact of various shape factors was investigated. The impact of a variety of active parameters, such as the magnetic parameter, viscosity coefficient, thermophoretic parameter, Brownian parameter, and nanofluid shape factor, on non dimensional velocity, temperature, and concentration profiles has been shown. The Nusselt number drops as the thermophoretic and Brownian parameters are increased, but the viscosity coefficient has the reverse tendency.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://***/licenses/by/ 4.0/).

关键词： Magnetohydrodynamic Hybrid nanofluid Brownian motion Thermophoresis radial basis function method Shape factor

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The numerical analysis of viscoelastic problems in signal propagation using a novel meshless Hermit-type RRKPM

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RESULTS IN PHYSICS 2024年 57卷

作者： Ma, Jichao Tai, Xin Ceyear Technol Co Ltd Shandong Elect Measurement Instrument Technol Inno Qingdao 266000 Peoples R China

Since meshless reproducing kernel particle method (RKPM) is easily affected by different kernel functions in numerical accuracy and stability, the Hermit-type function is introduced to the construction of trial function on boundary nodes. Meanwhile, the radial basis function is applied to establish the trial function in internal nodes, then a meshless Hermit-type radial basis function RKPM (Hermit-type RRKPM) is constructed. The advantage of this proposed method is that the numerical solution is more stable and the accuracy is higher. Furthermore, the meshless Hermit-type RRKPM is used to analyze viscoelastic problems. Finally, to illustrate the accuracy and stability, we compare the results of the proposed method and RRKPM with finite element method (FEM) solutions in solving viscoelastic problems.

关键词： Reproducing kernel particle method radial basis function method Meshless method Hermit-type radial basis function method Viscoelastic problems

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(3+1)-Dimensional time-fractional modified Burgers equation for dust ion-acoustic waves as well as its exact and numerical solutions

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MATHEMATICAL methodS IN THE APPLIED SCIENCES 2021年第10期44卷 8177-8196页

作者： Tian, Runhua Fu, Lei Ren, Yanwei Yang, Hongwei Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Shandong Peoples R China Shandong Univ Sci & Technol Coll Econ & Management Qingdao 266590 Shandong Peoples R China

In this paper, the theoretical model of dust ion-acoustic waves in collisionless, unmagnetized dust plasma is analyzed. According to the (3 + 1)-dimensional nonlinear dynamic propagation equations with the electron distribution in the presence of trapping particles and the kinetic equation of charge of dust particle, based on multiscale analysis and perturbation method, a new (3 + 1)-dimensional modified Burgers equation is constructed. Because of the space property of dust plasma, (3 + 1)-dimensional modified Burgers equation is more suitable than low-dimensional equation to describe the dust ion-acoustic waves. Furthermore, applying the semi-inverse method and the fractional variational principle, time-fractional modified Burgers equation is given, which owns potential value for comprehending the propagation feature of dust ion-acoustic waves in three-dimensional space. Following, the conservation laws of the time-fractional modified Burgers equation are discussed by using the Noether method. Finally, the shock wave solutions of the new model is obtained with the help of the G '/G-expansion method;meanwhile, the radial basis function method is also used to get the numerical solutions of the (3 + 1)-dimensional time-fractional modified Burgers equation.

关键词： (3+1)-dimensional time-fractional modified Burgers equation conservation laws dust ion-acoustic waves radial basis function method shock wave solution

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Boundary layer challenges: A comparative analysis of two efficient meshless approaches

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Partial Differential Equations in Applied Mathematics 2024年 10卷

作者： Alshammari, Abdulrahman Obaid Khan, Muhammad Nawaz Ahmad, Imtiaz Department of Mathematics College of Science Jouf University Sakaka 72388 Saudi Arabia Mathematics in Applied Sciences and Engineering Research Group Scientific Research Center Al-Ayen University Nasiriyah 64001 Iraq Institute of Informatics and Computing in Energy (IICE) Universiti Tenaga Nasional Kajang Selangor Malaysia

This article presents two meshless computational techniques: the radial basis function (RBF) method and the polynomial method, for numerically analyzing boundary layer problems, with a specific focus on singularly perturbed two-point boundary value problems. Both of these suggested meshless methods offer an advantage over globally supported meshless techniques, as they involve approximating derivatives by employing a constrained set of nodes located in the neighborhood of each collocation node. As a result, they demand significantly reduced computational effort compared to the globally supported collocation method. To assess the accuracy of these methods, we employ the maximum error norm, and the results are presented in the form of tables and graphs. The simulation results demonstrate that both approaches exhibit robust performance in addressing the investigated boundary layer problems. © 2024 The Author(s)

关键词： Boundary layer problems Meshless computational techniques Polynomial method radial basis function method

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