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

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About: Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_49
Description	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 and is 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 MPFA scheme which is faster than in the case of the reference finite volume scheme with 2nd order flux approximation. 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 and is 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 MPFA scheme which is faster than in the case of the reference finite volume scheme with 2nd order flux approximation. (en)
Title	Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth (en)
skos:prefLabel	Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth (en)
skos:notation	RIV/68407700:21340/13:00202841!RIV14-MSM-21340___
http://linked.open...avai/predkladatel	Fakulta jaderná a fyzikálně inženýrská
http://linked.open...avai/riv/aktivita	S Z
http://linked.open...avai/riv/aktivity	S, Z(MSM6840770010)
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Strachota, Pavel Beneš, Michal
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	68565
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/13:00202841
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	anisotropic diffusion; computational study; finite volume method; multipoint flux approximation; phase field model; microstructure growth (en)
http://linked.open.../riv/klicoveSlovo	anisotropic diffusion finite volume method computational study microstructure growth multipoint flux approximation phase field model
http://linked.open...ontrolniKodProRIV	[FAD223D24692]
http://linked.open...v/mistoKonaniAkce	Leicester
http://linked.open...i/riv/mistoVydani	Heidelberg
http://linked.open...i/riv/nazevZdroje	Numerical Mathematics and Advanced Applications 2011
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Beneš, Michal Strachota, Pavel
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2011-09-05 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Aplikovaná matematika v technických a fyzikálních vědách
number of pages	9 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-642-33134-3_49
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-642-33133-6
http://localhost/t...ganizacniJednotka	21340

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