Optimal Preconditioner for the Biconjugate Gradient Method

Ginkin, V.P.; Ganina, S.; Chernov, Kirill

doi:10.1080/00411450802522870

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…The mathematical method applied for numerical description and solution of phase transition (Stefan) problem at the liquids interface is considered in detail in [15]. The coordinate of the initial complete melting boundary (liquidus isotherm) is 48 mm from the "hot" end.…”

Section: The Numerical Model Appliedmentioning

confidence: 99%

Numerical study of convection-induced peritectic macro-segregation effect at the directional counter-gravity solidification of Ti–46Al–8Nb alloy

et al. 2011

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Section: The Numerical Model Appliedmentioning

confidence: 99%

Numerical study of convection-induced peritectic macro-segregation effect at the directional counter-gravity solidification of Ti–46Al–8Nb alloy

et al. 2011

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“…These equations were given in Boussinesq approximation form, allowing the melt description like an incompressible liquid. The method applied for numerical description and solution of phase transition (Stefan) problem at the liqudus interface is considered in detail in [12].…”

Section: The Numerical Model Appliedmentioning

confidence: 99%

Numerical Simulation of TiAl-Nb Alloy Solidification Experiment in TEM 01-3M Facility Aboard MAXUS 8

Kartavykh

Ganina

Grothe³

et al. 2010

MSF

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The problem of numerical modeling of directional solidification of TiAl refractory intermetallics aboard the MAXUS 8 sounding rocket is considered. The research is of relevance to the FP6 Integrated project IMPRESS (Intermetallic Materials Processing in Relation to Earth and Space Solidification). Attention is paid to columnar-to-equiaxed microstructure transition (CET) phenomenon and mushy zone evolution in Ti-45.9Al-8Nb (at %) alloy being processed in TEM 01-3M high-temperature (up to 17000C) furnace. In this three-zone resistive furnace the “bent” temperature profile is applied with two strongly different axial thermal gradients, presumably allowing the achieving of CET conditions along the sample of 160 mm length. Temperature profile evolution is defined by power-down furnace operation. 2D-numerical study of heat transfer and realtime-scale solidification dynamics of TiAl-Nb under zero gravity approximation is performed. The approaches used for solution of Navier-Stokes equations and phase transition (Stefan) problem are briefly described. The solidification time is shown to be satisfying the 12-minute microgravity limit aboard a MAXUS. The position and the time at which CET may be triggered are predicted and confirmed in line with the Hunt diagram. The comparison is performed of model predictions with the real microstructure of TiAl-Nb reference sample solidified on-ground in TEM 01-3M facility.

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“…The columnar structure of the ingot is formed at certain speeds. This is due to the different values of the temperature gradient arising at the boundary between the liquid and solid phases [7]. As was mentioned above [8], the following factors affect the value of the temperature gradients of a liquid-solid phase: thermophysical properties of the material; rate of crystallization; latent heat of crystallization; thermal convection that develops during melting.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Effect of the Electron-Beam Crucible Zone Melting of Metallurgical Silicon on Refining and Structure Formation of Ingots

Gokhman

Asnis

Piskun

et al. 2017

PCSS

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The paper presents the results of studies obtained with the development of the technology of electron-beam crucible impregnation of metallurgical silicon. It is shown that refining of silicon from background and dopant impurities in electron-beam crucible-free zone melting occurs by zone purification during melting and as a result of evaporation of impurities from the sample surface. The mathematical model and computational experiment were been performed to determine the temperature gradient at different rates of zone melting. It was found the diapason of temperature gradients, which provides the columnar structure of crystallites and the purification of the samplesdue the melting with the zone recrystallization procedure. The level of the resistivity of the ingots increases at the end.

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Optimal Preconditioner for the Biconjugate Gradient Method

Cited by 4 publications

References 3 publications

Numerical study of convection-induced peritectic macro-segregation effect at the directional counter-gravity solidification of Ti–46Al–8Nb alloy

Numerical study of convection-induced peritectic macro-segregation effect at the directional counter-gravity solidification of Ti–46Al–8Nb alloy

Numerical Simulation of TiAl-Nb Alloy Solidification Experiment in TEM 01-3M Facility Aboard MAXUS 8

Investigation of the Effect of the Electron-Beam Crucible Zone Melting of Metallurgical Silicon on Refining and Structure Formation of Ingots

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