Methods of Numerical Mathematics

Marchuk, G. I.

doi:10.1007/978-1-4613-8150-1

Cited by 258 publications

(193 citation statements)

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“…Inverse modeling is of major practical importance [Bennett, 1992; Marchuk, 1982] and reverse modeling of 3D diapiric structures is of special interest for earth scientists (e.g. 3D restoration of salt domes).…”

Section: Reverse Modeling Resultsmentioning

confidence: 99%

Forward and reverse modeling of the three‐dimensional viscous Rayleigh‐Taylor instability

Kaus

Podladchikov

2001

Geophysical Research Letters

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Section: Reverse Modeling Resultsmentioning

confidence: 99%

Forward and reverse modeling of the three‐dimensional viscous Rayleigh‐Taylor instability

Kaus

Podladchikov

2001

Geophysical Research Letters

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“…This will certainly be true if the Marchuk-Strang splitting procedure is used. This procedure, which was introduced in Marchuk (1968), see also Marchuk (1980Marchuk ( , 1982Marchuk ( , 1986Marchuk ( , 1988, and Strang (1968), is of order two. Therefore, it will be optimal to use this procedure together with second-order numerical methods.…”

Section: General Conclusion Related To Chaptermentioning

confidence: 99%

“…We are interested in the case where the method based on (5.55)-(5.57) is used in a combination with both the Marchuk-Strang splitting procedure, see Marchuk (1968Marchuk ( , 1980Marchuk ( , 1982Marchuk ( , 1986Marchuk ( , 1988) and Strang (1968) and the Richardson Extrapolation, see Faragó, Havasi and Zlatev (2010) and Richardson (1911Richardson ( , 1927. This combination is a new numerical method and we shall study some stability properties of the combined numerical method both in the general case when the Runge-Kutta methods is defined by (5.56)-(5.57) and in some particular cases.…”

Section: Some Introductory Remarksmentioning

confidence: 99%

Richardson Extrapolation

Zlatev¹,

Dimov²,

Faragó³

et al. 2017

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“…An operator-splitting technique (Glowinski and Le Tallec, 1989;Marchuk, 1982;and Samarskii, 1989), which follows SIMPLE algorithm described by Patankar (1980), is applied to efficiently resolve the problem of pressure-velocity decoupling.…”

Section: Discretization Of Governing Equationsmentioning

confidence: 99%

CFD Simulation of the Dispersion of Exhaust Gases in a Traffic Loaded Street of Astana, Kazakhstan

Akhatova

Kassymov

Kazmaganbetova

et al. 2016

J. Urb. and Environ. Engng

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Abstract:The aim of this paper is to consider one of the most traffic-loaded regions of Astana city (Kazakhstan) and to determine the concentration of carbon-monoxide (CO) in the air during the peak hours. CFD analysis based on the SolidWorks-EFD platform was used to simulate the dispersion of contaminants given the estimated emission rates and weather conditions at the crossroad of Bogenbay Batyr and Zhenis Avenues in Astana.Turbulence prediction was based on k-ε model with wall functions. The governing equations were discretized using the finite volume method and a 2 nd order spatial scheme. The mesh verification was based on 1% convergence criterion for a 50% of mesh density increment; air pressure near the wall of a selected building was chosen as the parameter to control the convergence. Numerical results are presented for prevailing conditions during all 4 seasons of the year, demonstrating that the highest levels of CO are recorded in summer and reach the values up to 11.2 ppm which are still lower than the maximum level admitted for humans. Nevertheless, obtained results show that Astana is gradually becoming a city that is likely to reach the critical levels of pollutants in the nearest future if control measures are not taken with enough anticipation. As for a future work, it is proposed to perform in-situ validation of specific scenarios to check and support the results obtained with CFD and to develop then specific policies for tackling the problem before it becomes evident.

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Methods of Numerical Mathematics

Cited by 258 publications

References 0 publications

Forward and reverse modeling of the three‐dimensional viscous Rayleigh‐Taylor instability

Forward and reverse modeling of the three‐dimensional viscous Rayleigh‐Taylor instability

Richardson Extrapolation

CFD Simulation of the Dispersion of Exhaust Gases in a Traffic Loaded Street of Astana, Kazakhstan

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