Exponential difference schemes for solving boundary-value problems for convection-diffusion type equations

Polyakov, S. V.; Karamzin, Yu. N.; Kudryashova, T. A.; Tsybulin, I. V.

doi:10.1134/s2070048217010124

Cited by 6 publications

(2 citation statements)

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“…,  -grid analogues of differential operators of gradient and Laplace [11]. The spatial approximation of the second and the third terms on the left-hand side of the discrete equation (10) was performed using exponential approximations proposed in [9,12,13].…”

Section: Methodsmentioning

confidence: 99%

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A novel parallel algorithm for 3D modelling electromagnetic purification of water

2018

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The computational fluid dynamic research in this work has focused on the problem of full-scale three-dimensional modelling water purification processes by the electromagnetic method. Presently, this method of purification was used in the final stage of processing for the production of ultrapure water. In spite of many field experiments, detailed data on such processes can be obtained only by the mathematical modelling. This way allows us to take into account many aspects, for example: real three-dimensional geometry, physical structure of the purification system, heterogeneous composition of the impurities, etc. And also, the mathematical modelling helps to optimize many parameters in order to improve a design of the purification system. Within the framework of the modelling problem, one of the important aspects is the correct description of the three-dimensional flow inside a specific purification system. For this purpose, various mathematical models and numerical approaches are implemented. In this paper, the flow calculation was realized on basis of the Navier-Stokes equations. * Corresponding author: kudryashova@imamod.ru MATEC Web of Conferences 210, 04027 (2018) https://doi.org/10.1051/matecconf/201821004027 CSCC 2018 results and make conclusions. And also, there are a few details about our future research.

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Section: Methodsmentioning

confidence: 99%

“…The hydrodynamic model has been supplemented with the electrostatic equations. The numerical realization is based on the methods of the theory of finite-difference schemes and on the original exponential schemes [9,12,13]. This paper has the following structure.…”

Section: Introductionmentioning

confidence: 99%