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research-article

A spacetime fractional phase-field model with tunable sharpness and decay behavior and its efficient numerical simulation

Authors:

Danping YangAuthors Info & Claims

Journal of Computational Physics, Volume 347, Issue C

Pages 20 - 38

https://doi.org/10.1016/j.jcp.2017.06.036

Published: 15 October 2017 Publication History

Abstract

We present a spacetime fractional AllenCahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the spacetime fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.

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Cited By

Liao HZhu XSun H(2024)Asymptotically Compatible Energy and Dissipation Law of the Nonuniform L2- Scheme for Time Fractional Allen–Cahn ModelJournal of Scientific Computing10.1007/s10915-024-02515-399:2Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1007/s10915-024-02515-3
Huang YChou LLei S(2023)Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion EquationsJournal of Scientific Computing10.1007/s10915-023-02259-696:1Online publication date: 5-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02259-6
Hou DZhu HXu C(2021)Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approachNumerical Algorithms10.1007/s11075-021-01068-y88:3(1077-1108)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s11075-021-01068-y
Show More Cited By

A spacetime fractional phase-field model with tunable sharpness and decay behavior and its efficient numerical simulation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 347, Issue C

October 2017

204 pages

ISSN:0021-9991

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 15 October 2017

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Cited By

Liao HZhu XSun H(2024)Asymptotically Compatible Energy and Dissipation Law of the Nonuniform L2- Scheme for Time Fractional Allen–Cahn ModelJournal of Scientific Computing10.1007/s10915-024-02515-399:2Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1007/s10915-024-02515-3
Huang YChou LLei S(2023)Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion EquationsJournal of Scientific Computing10.1007/s10915-023-02259-696:1Online publication date: 5-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02259-6
Hou DZhu HXu C(2021)Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approachNumerical Algorithms10.1007/s11075-021-01068-y88:3(1077-1108)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s11075-021-01068-y
Qin HLi DZhang Z(2021)A Novel Scheme to Capture the Initial Dramatic Evolutions of Nonlinear Subdiffusion EquationsJournal of Scientific Computing10.1007/s10915-021-01672-z89:3Online publication date: 10-Nov-2021
https://dl.acm.org/doi/10.1007/s10915-021-01672-z
Hou DXu C(2021)A Second Order Energy Dissipative Scheme for Time Fractional L Gradient Flows using SAV ApproachJournal of Scientific Computing10.1007/s10915-021-01667-w90:1Online publication date: 26-Nov-2021
https://dl.acm.org/doi/10.1007/s10915-021-01667-w
Liu HSheng CWang LYuan H(2021)On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen–Cahn EquationJournal of Scientific Computing10.1007/s10915-020-01363-186:2Online publication date: 7-Jan-2021
https://dl.acm.org/doi/10.1007/s10915-020-01363-1
Chen MLuan SLian Y(2021)Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equationsComputational Mechanics10.1007/s00466-020-01951-w67:2(601-617)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s00466-020-01951-w
Ren JLiao HZhang Z(2020)Superconvergence Error Estimate of a Finite Element Method on Nonuniform Time Meshes for Reaction–Subdiffusion EquationsJournal of Scientific Computing10.1007/s10915-020-01290-184:2Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1007/s10915-020-01290-1
Ji BLiao HZhang L(2020)Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equationAdvances in Computational Mathematics10.1007/s10444-020-09782-246:2Online publication date: 7-Apr-2020
https://dl.acm.org/doi/10.1007/s10444-020-09782-2

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