On Linear and unconditionally energy stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential
This work provides efficient and stable numerical methods for simulating phase separation in polymer blends, addressing a key computational challenge in materials science.
The authors developed first and second order linear, unconditionally energy stable numerical schemes for the Cahn-Hilliard equation with variable mobility and logarithmic Flory-Huggins potential, using the Invariant Energy Quadratization approach. Numerical simulations in 2D and 3D demonstrated stability, accuracy, and efficiency.
In this paper, we consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system numerically is how to develop proper temporal discretization for nonlinear terms in order to preserve the energy stability at the time-discrete level. We resolve this issue by developing a set of the first and second order time marching schemes based on a novel, called "Invariant Energy Quadratization" approach. Its novelty is that the proposed scheme is linear and symmetric positive definite because all nonlinear terms are treated semi-explicitly. We further prove all proposed schemes are unconditionally energy stable rigorously. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy and efficiency of the proposed schemes thereafter.