A Second Order, Linear, Unconditionally Stable, Crank-Nicolson-Leapfrog Scheme for Phase Field Models of Two-Phase Incompressible Flows

Daozhi Han; Nan Jiang

doi:10.1016/j.aml.2020.106521

A Second Order, Linear, Unconditionally Stable, Crank-Nicolson-Leapfrog Scheme for Phase Field Models of Two-Phase Incompressible Flows

Daozhi Han
, Nan Jiang

Missouri University of Science and Technology

Missouri University of Science and Technology

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

Abstract

In this article we propose a second order, linear, unconditionally stable, implicit-explicit scheme based on the Crank-Nicolson-Leapfrog discretization and the artificial compression method for solving phase field models of two-phase incompressible flows. We show that the scheme is unconditionally long-time stable. Numerical examples are provided to demonstrate the accuracy and long-time stability.

Original language	American English
Journal	Applied Mathematics Letters
Volume	108
DOIs	https://doi.org/10.1016/j.aml.2020.106521
State	Published - Oct 1 2020

Keywords

Artificial compression
Cahn-Hilliard-Navier-Stokes
Finite element method
Phase field models
Unconditional stability

Disciplines

Mathematics

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10.1016/j.aml.2020.106521License: Unspecified

https://doi.org/10.1016/j.aml.2020.106521

Cite this

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title = "A Second Order, Linear, Unconditionally Stable, Crank-Nicolson-Leapfrog Scheme for Phase Field Models of Two-Phase Incompressible Flows",

abstract = " In this article we propose a second order, linear, unconditionally stable, implicit-explicit scheme based on the Crank-Nicolson-Leapfrog discretization and the artificial compression method for solving phase field models of two-phase incompressible flows. We show that the scheme is unconditionally long-time stable. Numerical examples are provided to demonstrate the accuracy and long-time stability.",

keywords = "Artificial compression, Cahn-Hilliard-Navier-Stokes, Finite element method, Phase field models, Unconditional stability",

author = "Daozhi Han and Nan Jiang",

year = "2020",

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doi = "10.1016/j.aml.2020.106521",

language = "American English",

volume = "108",

journal = "Applied Mathematics Letters",

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T1 - A Second Order, Linear, Unconditionally Stable, Crank-Nicolson-Leapfrog Scheme for Phase Field Models of Two-Phase Incompressible Flows

AU - Han, Daozhi

AU - Jiang, Nan

PY - 2020/10/1

Y1 - 2020/10/1

N2 - In this article we propose a second order, linear, unconditionally stable, implicit-explicit scheme based on the Crank-Nicolson-Leapfrog discretization and the artificial compression method for solving phase field models of two-phase incompressible flows. We show that the scheme is unconditionally long-time stable. Numerical examples are provided to demonstrate the accuracy and long-time stability.

AB - In this article we propose a second order, linear, unconditionally stable, implicit-explicit scheme based on the Crank-Nicolson-Leapfrog discretization and the artificial compression method for solving phase field models of two-phase incompressible flows. We show that the scheme is unconditionally long-time stable. Numerical examples are provided to demonstrate the accuracy and long-time stability.

KW - Artificial compression

KW - Cahn-Hilliard-Navier-Stokes

KW - Finite element method

KW - Phase field models

KW - Unconditional stability

UR - https://scholarsmine.mst.edu/math_stat_facwork/1009

UR - https://doi.org/10.1016/j.aml.2020.106521

U2 - 10.1016/j.aml.2020.106521

DO - 10.1016/j.aml.2020.106521

M3 - Article

VL - 108

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

A Second Order, Linear, Unconditionally Stable, Crank-Nicolson-Leapfrog Scheme for Phase Field Models of Two-Phase Incompressible Flows

Abstract

Keywords

Disciplines

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