A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations

نویسندگان

  • Luis Cueto-Felgueroso
  • Jaime Peraire
چکیده

This paper presents a complete finite volume method for the Cahn–Hilliard and Kuramoto– Sivashinsky type of equations. The spatial discretization is high-order accurate and suitable for general unstructured grids. The time integration is addressed by means of implicit an implicit–explicit fourth order Runge–Kutta schemes, with error control and adaptive time-stepping. The outcome is a practical, accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations. The use of adaptive time-stepping is of paramount importance in problems governed by the Cahn–Hilliard model; an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps. In addition to driving the simulations efficiently, the time-adaptive procedure provides a quantitative (not just qualitative) characterization of the rich temporal scales present in phase separation processes governed by the Cahn–Hilliard phase-field model. 2008 Elsevier Inc. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Implicit-explicit multistep finite element methods for nonlinear parabolic problems

We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient, since their implementation requires at eac...

متن کامل

Application of Daubechies wavelets for solving Kuramoto-Sivashinsky‎ type equations

We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition‎. ‎Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method‎. ‎The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.    

متن کامل

A composite Runge–Kutta method for the spectral solution of semilinear PDE

A new composite Runge–Kutta (RK) method is proposed for semilinear partial differential equations such as Korteweg–de Vries, nonlinear Schrödinger, Kadomtsev– Petviashvili (KP), Kuramoto–Sivashinsky (KS), Cahn–Hilliard, and others having high-order derivatives in the linear term. The method uses Fourier collocation and the classical fourth-order RK method, except for the stiff linear modes, whi...

متن کامل

A Composite Runge–Kutta Method for theSpectral Solution of Semilinear PDEs

A new composite Runge–Kutta (RK) method is proposed for semilinear partial differential equations such as Korteweg–de Vries, nonlinear Schrödinger, Kadomtsev– Petviashvili (KP), Kuramoto–Sivashinsky (KS), Cahn–Hilliard, and others having high-order derivatives in the linear term. The method uses Fourier collocation and the classical fourth-order RK method, except for the stiff linear modes, whi...

متن کامل

Stability of periodic Kuramoto-Sivashinsky waves

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic travelingwave solutions of the generalized Kuramoto–Sivashinski equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Comput. Physics

دوره 227  شماره 

صفحات  -

تاریخ انتشار 2008