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<p>In this work, we develop and analyze a class of temporally up to third-order, unconditionally energy stable schemes for solving the nonlocal Cahn–Hilliard (NCH) equation. We begin with the Fourier pseudo-spectral approximation in the spatial direction. The temporal discretization is then carried out using an exponential-free Runge–Kutta (EFRK) framework, which is obtained by approximating certain exponential functions in the integrating factor Runge–Kutta scheme with Taylor polynomial. Based on the stabilization technique, we rigorously establish the energy stability of the EFRK schemes, which shows that the first- to third-order EFRK schemes have the ability to unconditionally preserve the original energy dissipation property. Numerical experiments are carried out to verify the convergence rate, mass conservation and energy stability. The long time simulations of coarsening dynamics are also performed to illustrate the power law of energy decay.</p>

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A Third-Order Energy Stable Exponential-Free Runge–Kutta Framework for the Nonlocal Cahn–Hilliard Equation

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • Xueqing Teng,
  • Hong Zhang

摘要

In this work, we develop and analyze a class of temporally up to third-order, unconditionally energy stable schemes for solving the nonlocal Cahn–Hilliard (NCH) equation. We begin with the Fourier pseudo-spectral approximation in the spatial direction. The temporal discretization is then carried out using an exponential-free Runge–Kutta (EFRK) framework, which is obtained by approximating certain exponential functions in the integrating factor Runge–Kutta scheme with Taylor polynomial. Based on the stabilization technique, we rigorously establish the energy stability of the EFRK schemes, which shows that the first- to third-order EFRK schemes have the ability to unconditionally preserve the original energy dissipation property. Numerical experiments are carried out to verify the convergence rate, mass conservation and energy stability. The long time simulations of coarsening dynamics are also performed to illustrate the power law of energy decay.