Modelling binary alloy solidification with adaptive mesh refinement

Parkinson, James R. G.; Martin, Daniel F.; Wells, Andrew J.; Katz, Richard F.

doi:10.1016/j.jcpx.2019.100043

Title: Modelling binary alloy solidification with adaptive mesh refinement

Journal Article · Wed Jan 01 00:00:00 EST 2020 · Journal of Computational Physics: X

DOI:https://doi.org/10.1016/j.jcpx.2019.100043· OSTI ID:1577402

; Martin, Daniel F.; Wells, Andrew J.; Katz, Richard F.

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231; IE141071

OSTI ID:: 1577402

Alternate ID(s):: OSTI ID: 1603566

Journal Information:: Journal of Computational Physics: X, Journal Name: Journal of Computational Physics: X Vol. 5 Journal Issue: C; ISSN 2590-0552

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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36 MATERIALS SCIENCE
binary alloy solidification
adaptive mesh refinement
mushy layer convection
finite volume

Title: Modelling binary alloy solidification with adaptive mesh refinement

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References (47)

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