Analytical and numerical solutions to Stefan problem in model of the glaciation dynamics of the multilayer cylinder in sea water

Mikova, V V; Kurbatova, G. I.; Ermolaeva, N. N.

doi:10.1088/1742-6596/929/1/012103

Cited by 7 publications

(4 citation statements)

References 7 publications

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“…In this sense, the considered model is close to the model of a phase transition with a moving boundary [36][37][38][39], the position of which is determined by the field profile. The position of the phase transition boundary is not determined in advance, but it is determined in the course of solution of such problems.…”

Section: Introductionmentioning

confidence: 85%

The smooth distributions of the surface states in a semi-bounded medium with an abruptly change in characteristics in dependence on the field amplitude

Савотченко

2021

Phys. Scr.

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The wave equation with the stepwise nonlinear coefficient on the semi-axis is considered. The boundary problems allowing to obtain the exact solutions of such nonlinear wave equation are proposed. Obtained solutions describe the features of the field localization near the surface covered with fully shielding film in the medium with an abruptly change in characteristics depending on the field. Five types of the surface states with the same structure but different amplitudes, phases, characteristic localization lengths and positions of the domain boundary are found. The features of the wave distributions and the influence of control parameters such as the threshold value of the switching field, surface amplitude and their derivatives on the wave characteristics are analyzed. The change in control parameters allows us to vary the position of the domain boundary.

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Section: Introductionmentioning

confidence: 85%

The smooth distributions of the surface states in a semi-bounded medium with an abruptly change in characteristics in dependence on the field amplitude

Савотченко

2021

Phys. Scr.

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“…It is known that all thermal and physical characteristics of growing sea ice depend on its salinity. The authors have previously proposed [15] the selection technique of a consistent set of thermo physical characteristics of growing sea ice. Based on these data, the following set of thermo physical characteristics and conditions was used in the calculations:…”

Section: Problem Statementmentioning

confidence: 99%

“…We estimate the error with which the Stefan condition (8) is satisfied in the numerical solution to the smoothed eq. (15). We write the integral equation of the balance of internal energy, ε , of the resting medium in the absence of sources (sinks) and external forces.…”

Section: Analysis Of the Cause Of The Increasing Error In The Calculamentioning

confidence: 99%

A parameters selection criterion of the numerical realisation of the continuous method for the Stefan problems

Kurbatova

Ermolaeva

2020

THERM SCI

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This paper suggests a selection criterion of the continuous method version for a numerical solution of the Stefan problem which would allow to calculate the phase transition boundary position with a required accuracy for a long period of time and would enable generalization to multidimensional problems. Despite a large number of works deal with the solution to the generalized Stefan problem by the continuous method, the choice of the smoothing interval value for numerical feasibility is not fully clear. A comparison of the calculation accuracy of the phase transition boundary position using different versions of the continuous method was carried out on an example of the well-known 1-D plane two-phase Stefan problem which possesses an analytical solution. The dependence of the total error of the numerical calculation of the phase transition boundary position on the value of the smearing interval is determined from the comparison of numerical and analytical solutions. An analysis of the reason for increase of this error with time at any choice of a constant smoothing interval is given. A version of the continuous method with a variable interval of the delta function smoothing, in which the proposed criterion is carried out, is discussed. The position of the phase transition boundary calculated proposed version matches the analytical solution with a required accuracy over a long period of time.

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“…Для определения начальных распределений температур T i 0 и максимальной толщины слоя льда сначала решается задача оледенения (постановка и алгоритм решения задачи приведены в работе [1]). Если температура окружающей воды увеличивается настолько, что для соответствующего ей значения величины теплового потока q 3 выполняется неравенство:…”

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Моделирование Динамики Таяния Льда На Внешней Поверхности Многослойного Морского Газопровода

Курбатова¹,

Никитчук²

2018

Научные Тенденции: Вопросы Точных И Технических Наук

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Analytical and numerical solutions to Stefan problem in model of the glaciation dynamics of the multilayer cylinder in sea water

Cited by 7 publications

References 7 publications

The smooth distributions of the surface states in a semi-bounded medium with an abruptly change in characteristics in dependence on the field amplitude

The smooth distributions of the surface states in a semi-bounded medium with an abruptly change in characteristics in dependence on the field amplitude

A parameters selection criterion of the numerical realisation of the continuous method for the Stefan problems

Моделирование Динамики Таяния Льда На Внешней Поверхности Многослойного Морского Газопровода

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