Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations

Saffarian, Marziyeh; Mohebbi, Akbar

doi:10.1016/j.matcom.2021.10.020

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…∂ λn ∂τ λn ω(ϑ, , τ) τ=0 τ λn (10) In order to elucidate the fundamental principles of the FRDTM, let us examine the following nonlinear partial differential equation expressed in an operator format [19]:…”

Section: Fractional Reduced Differential Transform Methods (Frdtm)mentioning

confidence: 99%

“…It has geographically and time-dependent coefficients for various input concentration pulses [9]. The Galerkin spectral element approach is used to provide an approximation of the Riesz space fractional in spatial directions, primarily to calculate the fractional advection-dispersion equation that applies in one and two dimensions of Riesz space [10]. For the alternative way to analyze the twodimensional time distributed-order diffusion-wave equation, authors have also applied the Legendre-Laguerre spectral method over a semi-infinite domain [11].…”

Section: Introductionmentioning

confidence: 99%

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Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

Maisuria,

Tandel,

Patel

2023

Axioms

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This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

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Section: Fractional Reduced Differential Transform Methods (Frdtm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

Maisuria,

Tandel,

Patel

2023

Axioms

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“…The mutual influence relationship and coordination degree between vehicle parts are very large and difficult to change under different parameter conditions. However, if the best matching state is to be achieved, it is necessary to ensure the mutual coordination between various parts to finally achieve the optimal overall function [9][10]. Therefore, the complex and changeable working environment of automobile engine has high requirements for its components and assembly process.…”

Section: Service Performance Of Automobile Enginementioning

confidence: 99%

Modeling and Design of Automotive Engine Performance Based on Finite Difference Method

2023

KME

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With the continuous development of the automobile industry, it has put forward higher requirements for the engine performance. In actual production, the failure of vehicle parts often occurs due to various factors. Especially for some parts with complex structure, they are more likely to fail. Therefore, in order to ensure the safe and reliable driving of vehicles and meet the use needs of vehicle owners and improve vehicle quality, this paper uses the finite difference method to model and analyze the design. Then, based on the finite difference method, this paper designed the automobile engine performance model, and tested the function of the model. The test results showed that the automobile engine performance modeling based on the finite difference method used a special process to coat silicon carbide powder on the inner wall of the cylinder block, which can improve its wear resistance and prolong its service life by 1~2 times. The high-grade refractory materials made of it are heat-resistant, small in size, light in weight and high in strength, Good energy-saving effect.

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“…By dropping (10) and substituting , n i j V with its numerical approximation , n i j v , we arrive at the given linearized finite difference scheme:…”

Section: Linearized Difference Schemementioning

confidence: 99%

“…Throughout recent decades, the SFADEs is presented as a practical model for the depiction of physical and natural phenomena arising in many areas of the applied sciences [1,2,3,4]. All kinds of numerical schemes have been proposed due to the extensive application of SFADEs across various fields, such as finite difference approximations [5,6], finite element method [7,8], finite volume method [9], spectral element method [10], meshless method [11] and the references therein. These methods, however, have been absorbed in the linear SFADEs.…”

Section: Introductionmentioning

confidence: 99%

A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations

Shan,

Wang

2023

Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023)

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Nonlinear Riesz space fractional advection-dispersion equations (SFADEs) find widespread applications in many fields, and numerical solutions are the primary means of solving such equations due to the complexity of nonlinear problems. A majority of the existing numerical techniques for solving nonlinear equations are based on three-level schemes, thereby leading to increased computational overheads and theoretical challenges. A novel approach is developed to solve twodimensional nonlinear Riesz SFADEs, which employs a two-level linearized finite difference method and incorporates state-of-the-art linearization techniques. The proposed approach involves using the Crank-Nicolson approach to process the time component and approximating the Riesz space fractional derivative using the weighted and shifted Grünwald difference (WSGD) formula. The resulting difference scheme is observed to exhibit second-order convergence in both temporal and spatial coordinates. The efficiency and accuracy of the proposed method are confirmed by conducting numerical experiments.

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Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations

Cited by 9 publications

References 30 publications

Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

Modeling and Design of Automotive Engine Performance Based on Finite Difference Method

A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations

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