Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00202841" target="_blank" >RIV/68407700:21340/13:00202841 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_49" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_49</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-642-33134-3_49" target="_blank" >10.1007/978-3-642-33134-3_49</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth

Popis výsledku v původním jazyce

As an alternative to the sharp interface formulation, the phase field approach is a widely used technique for modeling phase transitions. The governing system of reaction-diffusion equations captures the instability of the underlying physical problem andis capable of modeling the evolution of complicated crystal shapes during solidification of an undercooled melt. For its numerical solution, we propose our novel anti-diffusive multipoint flux approximation (MPFA) finite volume scheme on a Cartesian mesh. The scheme is verified against the analytical solution of the modified sharp interface model. Experimental order of convergence (EOC) is measured for the temperature field in the usual norms. In addition, EOC is also obtained for the phase interface through approximating the volume of the symmetric difference of the solid phase subdomains. In the anisotropic cases including unusual higher order symmetries, computational studies with various settings also confirm convergence of our MPF

Název v anglickém jazyce

Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth

Popis výsledku anglicky

As an alternative to the sharp interface formulation, the phase field approach is a widely used technique for modeling phase transitions. The governing system of reaction-diffusion equations captures the instability of the underlying physical problem andis capable of modeling the evolution of complicated crystal shapes during solidification of an undercooled melt. For its numerical solution, we propose our novel anti-diffusive multipoint flux approximation (MPFA) finite volume scheme on a Cartesian mesh. The scheme is verified against the analytical solution of the modified sharp interface model. Experimental order of convergence (EOC) is measured for the temperature field in the usual norms. In addition, EOC is also obtained for the phase interface through approximating the volume of the symmetric difference of the solid phase subdomains. In the anisotropic cases including unusual higher order symmetries, computational studies with various settings also confirm convergence of our MPF

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Numerical Mathematics and Advanced Applications 2011

ISBN

978-3-642-33133-6

ISSN

—

e-ISSN

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Počet stran výsledku

9

Strana od-do

459-467

Název nakladatele

Springer

Místo vydání

Heidelberg

Místo konání akce

Leicester

Datum konání akce

5. 9. 2011

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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