A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem

Shukla, Anand; Singh, Akhilesh Kumar; Singh, P.

doi:10.5923/j.ajcam.20110102.13

Cited by 23 publications

(7 citation statements)

References 6 publications

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“…The governing equation cannot be easily solved by analytical methods. Hence, a numerical approach is necessary to solve the vorticity transport equation of droplets in the facemasks (Ghia et al 1982 ; Tsega and Katiyar 2018 ; Harlow and Welch 1965 ; Shukla et al 2011 ). And accordingly, a finite-difference method has been applied to the Poisson equation consisting of the droplets dynamics together with the time of the dispersion of cough droplets in facemasks.…”

Section: The Numerical Results and Discussionmentioning

confidence: 99%

Modeling and Simulations of Moving Droplets in Relation to SARS-CoV-19 Generated by Respiratory System

et al. 2022

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Contemporary issues such as epidemics and the prevalence of infectious indicate that there is a pressing need to better understand the dynamics of transmission in air and facemasks. Consistent with previous literature, coronavirus disease (COVID-2019) is caused by the novel virus SARS-CoV-2. Coronavirus adds a new element to fluid fragmentation leading to respiratory droplets and which are transmitted via air during coughing, sneezing and talking. The behavior of virus-laden droplets of saliva particles arising from a human cough is described by Navier–Stokes equation for turbulent flow. The predicted velocity and pressure for droplets flow with time are presented. Hence, wall-normal profiles of velocity, pressure and concentration are obtained from boundary-layer approximations and the Navier–Stokes equations are solved on a two-dimensional shell mesh. The purpose of this study is to provide a perspective on the role of masks in the COVID-19 pandemic with an emphasis on the mechanism of droplet leakage and the droplet dispersion in this masks medical non-pharmaceutical intervention.

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Section: The Numerical Results and Discussionmentioning

confidence: 99%

Modeling and Simulations of Moving Droplets in Relation to SARS-CoV-19 Generated by Respiratory System

et al. 2022

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“…The TES tank models are based on the one-dimensional convection-diffusion-reaction equation. Previous case studies have shown that a one-dimensional approach can represent the behavior of water tanks (Appadu and Appadu, 2013;Karahan, 2006;Shukla et al, 2011), PCM tanks (Hu and Argyropoulos, 1996;Lo Brano et al, 2014), and TCM tanks (Finck, C.J. et al;Pesaran et al, 2016).…”

Section: Methodsmentioning

confidence: 99%

Performance Maps for the Control of Thermal Energy Storage

Finck

Li²,

Zeiler

2017

Building Simulation Conference Proceedings

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“…The purpose of solving this numerical example is, to compare the numerical results of our proposed upwind approach with most popular and commonly used ( central differencing form of finite volume method) numerical form of finite volume method [10,11,12,13]. Obtained numerical solution and maximum error produced by both numerical scheme are listed below, For case-1 of convection dominancy, numerical results of our proposed approach and central differencing approach are shown in Figure 9.…”

Section: Example-2mentioning

confidence: 99%

“…The finite difference method (FDM) studied by [10,11,12,13,14,15,16] is a domain discretising technique, convert the governing problem into a difference equation. The functional values are approximated at the nodes of the network.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of convection-dominated diffusion problem using modified upwind finite volume method

Hussain,

Zheng,

Eyaya

2024

Preprint

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In this paper, an attempt has been made to developed a numerical scheme for numerical approximation of the convection-diffusion problem in convection dominant situations. Applying Lagrange interpolation technique, new expressions are obtained to approximate the variable at spatial interfaces of the computational domain. Subsequently, these interface approximations are used to developed a numerical scheme based on upwind approach in the finite volume method. Crank-Nicolson technique is used for the approximation along temporal direction. This newly constructed numerical scheme is unconditionally stable with second order accuracy along space and time both. The numerical experiments are performed using the proposed upwind approach and numerical results confirm the theoretical algorithm. Numerical results produce by our constructed numerical are compared with conventional finite volume method. This comparison indicates for convection dominant phenomena the numerical solution of conventional finite volume method contains with non-physical oscillations where are our proposed numerical schemes give a high accurate and stable solution.

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A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem

Cited by 23 publications

References 6 publications

Modeling and Simulations of Moving Droplets in Relation to SARS-CoV-19 Generated by Respiratory System

Modeling and Simulations of Moving Droplets in Relation to SARS-CoV-19 Generated by Respiratory System

Performance Maps for the Control of Thermal Energy Storage

Numerical solution of convection-dominated diffusion problem using modified upwind finite volume method

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