Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique

TL;DR

This paper introduces an efficient, energy-stable numerical scheme combining spectral deferred correction and convex splitting for the Landau-Brazovskii model, effectively simulating complex microphase structures with conserved mass.

Contribution

It develops a novel mass conservative and energy stable numerical scheme using spectral deferred correction and convex splitting for the Landau-Brazovskii model.

Findings

The scheme preserves energy stability and mass conservation.

Numerical experiments demonstrate high efficiency in 2D and 3D simulations.

The adaptive correction reduces computational cost.

Abstract

The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.