Unconditionally Energy Stable Second Order Numerical Scheme for a Microemulsion model

2025/03/30 by Sharma, Natasha S., Tierra, Giordano
#35K51 #35M13 #35Q35 #65M12 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2503.23516

Abstract

We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic. We show that by considering a suitable midpoint approximation for the nonlinear terms in the differential equation, we obtain an unconditionally energy-stable numerical scheme that is second-order in time. We demonstrate that our proposed numerical scheme satisfies these key properties for a wide range of physical parameters in two and three dimensions. Moreover, we present the results of a numerical study to report on the impact of each physical parameter on the behavior of the dynamics of the phase transitions, which are in agreement with the experimental observations.

Related

• Numerical Approximations for the Cahn-Hilliard phase field model of the binary fluid-surfactant system
• Numerical approximations for the binary Fluid-Surfactant Phase Field Model with fluid flow: Second-order, Linear, Energy stable schemes
• Second order stabilized semi-implicit scheme for the Cahn-Hilliard model with dynamic boundary conditions
• Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints
• A ternary mixture model with dynamic boundary conditions