1,047 research outputs found
A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation
We propose a novel second order in time numerical scheme for
Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme
is based on second order convex-splitting for the Cahn-Hilliard equation and
pressure-projection for the Navier-Stokes equation. We show that the scheme is
mass-conservative, satisfies a modified energy law and is therefore
unconditionally stable. Moreover, we prove that the scheme is uncondition- ally
uniquely solvable at each time step by exploring the monotonicity associated
with the scheme. Thanks to the weak coupling of the scheme, we design an
efficient Picard iteration procedure to further decouple the computation of
Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by
the mixed finite element method. Ample numerical experiments are performed to
validate the accuracy and efficiency of the numerical scheme
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
How to develop efficient numerical schemes while preserving the energy
stability at the discrete level is a challenging issue for the three component
Cahn-Hilliard phase-field model. In this paper, we develop first and second
order temporal approximation schemes based on the "Invariant Energy
Quadratization" approach, where all nonlinear terms are treated
semi-explicitly. Consequently, the resulting numerical schemes lead to a
well-posed linear system with the symmetric positive definite operator to be
solved at each time step. We rigorously prove that the proposed schemes are
unconditionally energy stable. Various 2D and 3D numerical simulations are
presented to demonstrate the stability and the accuracy of the schemes
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