Finite element based hybrid techniques for advection-diffusion-reaction processes

Sarı, Murat; Tunc, Huseyin

doi:10.11121/ijocta.01.2018.00452

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Consider the advection-diffusion process with the choices of V=1, D=0.01 and β=0 in the ADR equation (1) for which the exact solution is given by (Sari and Tunc, 2018)…”

Section: Numerical Experimentsmentioning

confidence: 99%

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An implicit-explicit local method for parabolic partial differential equations

Tunc

Sarı

2021

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PurposeThe purpose of this article is to derive an implicit-explicit local differential transform method (IELDTM) in dealing with the spatial approximation of the stiff advection-diffusion-reaction (ADR) equations.Design/methodology/approachA direction-free numerical approach based on local Taylor series representations is designed for the ADR equations. The differential equations are directly used for determining the local Taylor coefficients and the required degrees of freedom is minimized. The complete system of algebraic equations is constructed with explicit/implicit continuity relations with respect to direction parameter. Time integration of the ADR equations is continuously utilized with the Chebyshev spectral collocation method.FindingsThe IELDTM is proven to be a robust, high order, stability preserved and versatile numerical technique for spatial discretization of the stiff partial differential equations (PDEs). It is here theoretically and numerically shown that the order refinement (p-refinement) procedure of the IELDTM does not affect the degrees of freedom, and thus the IELDTM is an optimum numerical method. A priori error analysis of the proposed algorithm is done, and the order conditions are determined with respect to the direction parameter.Originality/valueThe IELDTM overcomes the known disadvantages of the differential transform-based methods by providing reliable convergence properties. The IELDTM is not only improving the existing Taylor series-based formulations but also provides several advantages over the finite element method (FEM) and finite difference method (FDM). The IELDTM offers better accuracy, even when using far less degrees of freedom, than the FEM and FDM. It is proven that the IELDTM produces solutions for the advection-dominated cases with the optimum degrees of freedom without producing an undesirable oscillation.

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“…Consider the advection-diffusion process with the choices of V=1, D=0.01 and β=0 in the ADR equation (1) for which the exact solution is given by (Sari and Tunc, 2018)…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In Table 1, the present IELDTM-ChCM algorithm has been compared with the FEMs (Sari and Tunc, 2018; Kadalbajoo and Arora, 2010), the FDM (Sari et al , 2010) and the exact solution. The degrees of freedom ( dof ) of all numerical algorithms have been presented.…”

Section: Numerical Experimentsmentioning

confidence: 99%

An implicit-explicit local method for parabolic partial differential equations

Tunc

Sarı

2021

Self Cite

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“…The study of the transport equation, also known as advection-diffusion-reaction equation remains an active field of research since such an equation plays a fundamental role in a wide variety of modeling problems. Some of them are related to aerodynamics, meteorology, oceanography, hydrology, and chemical engineering [1]. In general terms, the transport equation describes how the concentration of one or more elements (pollutants, heat, etc.)…”

Section: Introductionmentioning

confidence: 99%

An Implementation of the Finite Differences Method for the Two-Dimensional Rectangular Cooling Fin Problem

Rodrigues¹

2019

IJITCS

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The transport or advection-diffusion-reaction equation is a well-known partial differential equation employed to model several types of flux problems. The cooling fin problem is a particular case of such an equation. This work presents a straightforward model for the rectangular cooling fin in a problem. The model was based on the finite differences numerical method and an efficient implementation was developed in a high-level mathematical programming language. The accuracy was evaluated with different granularity levels of meshes, and two distinct boundary conditions are compared. In the first one, only prescribed temperatures are assumed at the four tips of the domain. For the second scenario, it is assumed a heat flux at one tip of a fin with the same geometrical shape. The achieved solutions produced by the algorithm were able to depict the temperature along the whole fin surface accurately. Furthermore, the algorithm reaches relevant performance for meshes up to 4257 points where the CPU time was about 33 seconds.

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Initial data identification in advection–diffusion processes via a reversed fixed‐point iteration method

Cosgun

Sarı

2022

Math Methods in App Sciences

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In the present study, a novel method called the reversed fixed‐point iteration method (RFPIM) is applied to obtain numerical responses of the advection–diffusion mechanisms. Heretofore, the RFPIM has been employed to find out unstable equilibria of nonlinear mappings defined on Banach spaces. The current paper implements the method to recover the initial data from the final data. The method has been tested under measurements including different levels of noise such as 5%, 10%, 30%, 50%, and 100% in the final time data, and the results indicate that the present technique could be regarded as a powerful tool in handling such inverse problems.

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Finite element based hybrid techniques for advection-diffusion-reaction processes

Cited by 4 publications

References 14 publications

An implicit-explicit local method for parabolic partial differential equations

An implicit-explicit local method for parabolic partial differential equations

An Implementation of the Finite Differences Method for the Two-Dimensional Rectangular Cooling Fin Problem

Initial data identification in advection–diffusion processes via a reversed fixed‐point iteration method

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