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

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A parameters selection criterion of the numerical realisation of the continuous method for the stefan problems. / Kurbatova , Galina I.; Ermolaeva , Nadezhda N.

In: Thermal Science, Vol. 24, 2020, p. 2267-2277.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{6963b04a6f804f30a5463e4c016490e2,

title = "A parameters selection criterion of the numerical realisation of the continuous method for the stefan problems",

abstract = "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.",

keywords = "Choice of the delta function smearing interval, Glaciation, Numerical solutions, Stefan problem, The continuous method version",

author = "Kurbatova, {Galina I.} and Ermolaeva, {Nadezhda N.}",

year = "2020",

doi = "10.2298/TSCI190121306K",

language = "English",

volume = "24",

pages = "2267--2277",

journal = "Thermal Science",

issn = "0354-9836",

publisher = "Vinca Inst Nuclear Sci",

}

RIS

TY - JOUR

T1 - A parameters selection criterion of the numerical realisation of the continuous method for the stefan problems

AU - Kurbatova , Galina I.

AU - Ermolaeva , Nadezhda N.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Choice of the delta function smearing interval

KW - Glaciation

KW - Numerical solutions

KW - Stefan problem

KW - The continuous method version

UR - http://www.scopus.com/inward/record.url?scp=85086858291&partnerID=8YFLogxK

U2 - 10.2298/TSCI190121306K

DO - 10.2298/TSCI190121306K

M3 - Article

AN - SCOPUS:85086858291

VL - 24

SP - 2267

EP - 2277

JO - Thermal Science

JF - Thermal Science

SN - 0354-9836

ER -

ID: 49523294