Solving second order non-linear parabolic PDEs using generalized finite difference method (GFDM)

Ureña, Francisco; Gavete, L.; García, A.; Benito, Juan José; Vargas, A.M.

doi:10.1016/j.cam.2018.02.016

Cited by 49 publications

(22 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…J. Chen et al then calculated electromagnetic field using the GFDM to reduce the computation time [25]. Currently, GFDM has been used in field calculation problems such as heat transfer and fluid mechanics to increase the calculation accuracy of a relatively small area in a large field domain [26,27].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Dry Band Formation and Arcing Processes on the Polluted Composite Insulator Surface

Gao

2019

Energies

View full text Add to dashboard Cite

This paper modeled the dry band formation and arcing processes on the composite insulator surface to investigate the mechanism of dry band arcing and optimize the insulator geometry. The model calculates the instantaneous electric and thermal fields before and after arc initialization by a generalized finite difference time domain (GFDTD) method. This method improves the field calculation accuracy at a high precision requirement area and reduces the computational complexity at a low precision requirement area. Heat transfer on the insulator surface is evaluated by a thermal energy balance equation to simulate a dry band formation process. Flashover experiments were conducted under contaminated conditions to verify the theoretical model. Both simulation and experiments results show that dry bands were initially formed close to high voltage (HV) and ground electrodes because the electric field and leakage current density around electrode are higher when compared to other locations along the insulator creepage distance. Three geometry factors (creepage factor, shed angle, and alternative shed ratio) were optimized when the insulator creepage distances remained the same. Fifty percent flashover voltage and average duration time from dry band generation moment to flashover were calculated to evaluate the insulator performance under contaminated conditions. This model analyzes the dry band arcing process on the insulator surface and provides detailed information for engineers in composite insulator design.

show abstract

Section: Introductionmentioning

confidence: 99%

Modeling of Dry Band Formation and Arcing Processes on the Polluted Composite Insulator Surface

Gao

2019

Energies

View full text Add to dashboard Cite

show abstract

“…In [5], new nonstandard finite difference technique is implemented for solving fractional Navier stokes equations with stability and convergence. The convergence of generalized finite difference method for PDEs can be seen in [6]. The work of the differencing technique for some problem can be seen in [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A new class of A-stable numerical techniques for ordinary differential equations: Application to boundary-layer flow

Nawaz

Arif

2021

THERM SCI

View full text Add to dashboard Cite

The present attempt is made to propose a new class of numerical techniques for finding numerical solutions of ODEs. The proposed numerical techniques are based on interpolation of a polynomial. Currently constructed numerical techniques use the additional information(s) of derivative(s) on particular grid point(s). The advantage of the presently proposed numerical techniques is that these techniques are implemented in one step and can provide highly accurate solution and can be constructed on fewer amounts of grid points but has the disadvantage of finding derivative(s). It is to be noted that the high order techniques can be constructed using just two grid points. Presently proposed fourth-order technique is A-stable but not L-stable. The order and maximum absolute error are found for a fourth-order technique. The fourth-order technique is employed to solve the Darcy-Forchheimer fluid flow problem which is transformed further to a third-order nonlinear boundary value problem on the semi-infinite domain.

show abstract

“…In this paper we propose the Generalized Finite Difference Method (GFDM). This meshless method has been recently proved to solve with accuracy highly nonlinear PDEs, see [10,11]. In [2], the authors obtained conditional convergence for the parabolic-elliptic case of system (1) for d = a 2 = 0, a 0 = a 1 and m = α = γ = 1.…”

Section: Introductionmentioning

confidence: 99%

Solving a reaction–diffusion system with chemotaxis and non-local terms using Generalized Finite Difference Method. Study of the convergence

Benito

García

Gavete³

et al. 2021

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper a parabolic-parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the twodimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic-elliptic model, as generalized by the parabolic-parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms.

show abstract

Solving second order non-linear parabolic PDEs using generalized finite difference method (GFDM)

Cited by 49 publications

References 17 publications

Modeling of Dry Band Formation and Arcing Processes on the Polluted Composite Insulator Surface

Modeling of Dry Band Formation and Arcing Processes on the Polluted Composite Insulator Surface

A new class of A-stable numerical techniques for ordinary differential equations: Application to boundary-layer flow

Solving a reaction–diffusion system with chemotaxis and non-local terms using Generalized Finite Difference Method. Study of the convergence

Contact Info

Product

Resources

About