An unconditional energy stable numerical scheme for fluid-surfactant system with data assimilation method

초록

This paper investigates the dynamics of fluid-surfactant systems by incorporating a data assimilation term into the governing equations, enabling data corrections to the system evolution based on observed data. This approach allows for accurate tracking of the system behavior, addressing the challenges posed by the fluid-surfactant interaction. To solve the modified system, we develop an unconditional energy stable and efficient numerical scheme that combines the Crank-Nicolson method for time discretization with Lagrange multipliers. We provide a rigorous stability proof for the scheme, ensuring reliable solutions in simulations. Through extensive numerical experiments, we validate the energy dissipation properties of the scheme, investigate its performance under various initial conditions, and analyze the impact of temporal and spatial sampling rates on the assimilation results. The robustness of the method is demonstrated in simulations of shear flow and droplet coalescence. By incorporating the observed data, our approach offers a useful framework for simulating and predicting the dynamics of such systems, with potential applications in material science and engineering.

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