Numerical Analysis of Second Order, Fully Discrete Energy Stable Schemes for Phase Field Models of Two-Phase Incompressible Flows
In this paper, we propose several second order in time, fully discrete, linear and nonlinear numerical schemes for solving the phase field model of two-phase incompressible flows, in the framework of finite element method. The schemes are based on the second order Crank-Nicolson method for time discretization, projection method for Navier-Stokes equations, as well as several implicit-explicit treatments for phase field equations. The energy stability and unique solvability of the proposed schemes are proved. Ample numerical experiments are performed to validate the accuracy and efficiency of the proposed schemes.
D. Han et al., "Numerical Analysis of Second Order, Fully Discrete Energy Stable Schemes for Phase Field Models of Two-Phase Incompressible Flows," Journal of Scientific Computing, vol. 70, no. 3, pp. 965 - 989, Springer Verlag, Mar 2017.
The definitive version is available at https://doi.org/10.1007/s10915-016-0279-5
Mathematics and Statistics
Keywords and Phrases
Convergence of numerical methods; Incompressible flow; Navier Stokes equations; Numerical methods; Phase interfaces; Two phase flow; Energy stability; Explicit treatments; Numerical experiments; Phase field equation; Phase field models; Phase fields; Projection method; Time discretization; Finite element method; Navier-Stokes; Stability
International Standard Serial Number (ISSN)
Article - Journal
© 2017 Springer Verlag, All rights reserved.
01 Mar 2017