Development of a 2-D algorithm to simulate convection and phase transition efficiently

Katherine J. Evans; D. A. Knoll; Michael Pernice

doi:10.1016/j.jcp.2006.03.025

Development of a 2-D algorithm to simulate convection and phase transition efficiently

Katherine J. Evans, D. A. Knoll, Michael Pernice

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

23 Scopus citations

Abstract

We develop a Jacobian-Free Newton-Krylov (JFNK) method for the solution of a two-dimensional convection phase change model using the incompressible Navier-Stokes equation set and enthalpy as the energy conservation variable. The SIMPLE algorithm acts as a physics-based preconditioner to JFNK. This combined algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for two benchmark problems of phase change convection of a pure material, one melting and one freezing. The JFNK-SIMPLE method is shown to be more efficient per time step and more robust at larger time steps. Overall CPU savings of more than an order of magnitude are realized.

Original language	English
Pages (from-to)	404-417
Number of pages	14
Journal	Journal of Computational Physics
Volume	219
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2006.03.025
State	Published - Nov 20 2006
Externally published	Yes

Funding

This work was carried out under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. W-7405-ENG-36 (LA-UR-06-0051).

Keywords

Newton-Krylov
Phase change convection
SIMPLE preconditioner

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10.1016/j.jcp.2006.03.025

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abstract = "We develop a Jacobian-Free Newton-Krylov (JFNK) method for the solution of a two-dimensional convection phase change model using the incompressible Navier-Stokes equation set and enthalpy as the energy conservation variable. The SIMPLE algorithm acts as a physics-based preconditioner to JFNK. This combined algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for two benchmark problems of phase change convection of a pure material, one melting and one freezing. The JFNK-SIMPLE method is shown to be more efficient per time step and more robust at larger time steps. Overall CPU savings of more than an order of magnitude are realized.",

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T1 - Development of a 2-D algorithm to simulate convection and phase transition efficiently

AU - Evans, Katherine J.

AU - Knoll, D. A.

AU - Pernice, Michael

PY - 2006/11/20

Y1 - 2006/11/20

N2 - We develop a Jacobian-Free Newton-Krylov (JFNK) method for the solution of a two-dimensional convection phase change model using the incompressible Navier-Stokes equation set and enthalpy as the energy conservation variable. The SIMPLE algorithm acts as a physics-based preconditioner to JFNK. This combined algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for two benchmark problems of phase change convection of a pure material, one melting and one freezing. The JFNK-SIMPLE method is shown to be more efficient per time step and more robust at larger time steps. Overall CPU savings of more than an order of magnitude are realized.

AB - We develop a Jacobian-Free Newton-Krylov (JFNK) method for the solution of a two-dimensional convection phase change model using the incompressible Navier-Stokes equation set and enthalpy as the energy conservation variable. The SIMPLE algorithm acts as a physics-based preconditioner to JFNK. This combined algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for two benchmark problems of phase change convection of a pure material, one melting and one freezing. The JFNK-SIMPLE method is shown to be more efficient per time step and more robust at larger time steps. Overall CPU savings of more than an order of magnitude are realized.

KW - Newton-Krylov

KW - Phase change convection

KW - SIMPLE preconditioner

UR - https://www.scopus.com/pages/publications/33750304690

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DO - 10.1016/j.jcp.2006.03.025

M3 - Article

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SN - 0021-9991

VL - 219

SP - 404

EP - 417

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Development of a 2-D algorithm to simulate convection and phase transition efficiently

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