Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

Keunsoo Park; Marc Gerritsma; Maria Fernandino

doi:10.1007/978-3-319-73441-5_13

Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

Keunsoo Park^*, Marc Gerritsma, Maria Fernandino

^*Corresponding author for this work

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (Scopus)

Abstract

There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C¹ Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.

Original language	English
Title of host publication	Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers
Publisher	Springer
Pages	128-136
Number of pages	9
Volume	10665 LNCS
ISBN (Print)	9783319734408
DOIs	https://doi.org/10.1007/978-3-319-73441-5_13
Publication status	Published - 2018
Event	11th International Conference on Large-Scale Scientific Computations - Sozopol, Bulgaria Duration: 11 Sept 2017 → 15 Sept 2017 Conference number: 11

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10665 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Conference

Conference	11th International Conference on Large-Scale Scientific Computations
Abbreviated title	LSSC 2017
Country/Territory	Bulgaria
City	Sozopol
Period	11/09/17 → 15/09/17

Keywords

Adaptive
Cahn-Hilliard
Least-square
Parallel computation
Phase-field

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10.1007/978-3-319-73441-5_13

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Park, K., Gerritsma, M., & Fernandino, M. (2018). Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method. In Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers (Vol. 10665 LNCS, pp. 128-136). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10665 LNCS). Springer. https://doi.org/10.1007/978-3-319-73441-5_13

Park, Keunsoo ; Gerritsma, Marc ; Fernandino, Maria. / Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method. Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers. Vol. 10665 LNCS Springer, 2018. pp. 128-136 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.",

keywords = "Adaptive, Cahn-Hilliard, Least-square, Parallel computation, Phase-field",

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Park, K, Gerritsma, M & Fernandino, M 2018, Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method. in Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers. vol. 10665 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10665 LNCS, Springer, pp. 128-136, 11th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, 11/09/17. https://doi.org/10.1007/978-3-319-73441-5_13

Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method. / Park, Keunsoo; Gerritsma, Marc; Fernandino, Maria.
Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers. Vol. 10665 LNCS Springer, 2018. p. 128-136 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10665 LNCS).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

AU - Park, Keunsoo

AU - Gerritsma, Marc

AU - Fernandino, Maria

N1 - Conference code: 11

PY - 2018

Y1 - 2018

N2 - There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.

AB - There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.

KW - Adaptive

KW - Cahn-Hilliard

KW - Least-square

KW - Parallel computation

KW - Phase-field

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U2 - 10.1007/978-3-319-73441-5_13

DO - 10.1007/978-3-319-73441-5_13

M3 - Conference contribution

AN - SCOPUS:85041713451

SN - 9783319734408

VL - 10665 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 128

EP - 136

BT - Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers

PB - Springer

T2 - 11th International Conference on Large-Scale Scientific Computations

Y2 - 11 September 2017 through 15 September 2017

ER -

Park K, Gerritsma M, Fernandino M. Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method. In Large-Scale Scientific Computing - 11th International Conference, LSSC 2017, Revised Selected Papers. Vol. 10665 LNCS. Springer. 2018. p. 128-136. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-73441-5_13

Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

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