# Numerical Methods for a System of Coupled Cahn-Hilliard Equations

## TL;DR

This paper develops and tests numerical methods for a coupled system of Cahn-Hilliard equations modeling phase separation in polymer blends, combining existing schemes and analyzing their behavior through simulations.

## Contribution

It introduces a novel combination of numerical schemes tailored for coupled Cahn-Hilliard equations and demonstrates their effectiveness through detailed simulations.

## Key findings

- Numerical methods accurately capture phase separation dynamics.
- Parameter variations significantly affect the numerical solutions.
- The approach is verified through comprehensive tests.

## Abstract

In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our approach, we present some tests and a detailed description of the numerical solutions' behaviour obtained by varying the values of the parameters.