An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model

TL;DR

This paper introduces a novel upwind Discontinuous Galerkin scheme for the convective Cahn-Hilliard model that maintains the maximum principle, reduces oscillations, and is validated through numerical experiments and comparisons.

Contribution

The paper presents a new upwind DG scheme that preserves the maximum principle for the convective Cahn-Hilliard model with degenerate mobility, addressing a challenging numerical approximation problem.

Findings

The scheme preserves the maximum principle in numerical simulations.

Numerical experiments confirm the theoretical properties of the scheme.

Comparisons show advantages over existing methods.

Abstract

The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, even more if considering additional transport terms. In this work we present a new upwind Discontinuous Galerkin scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the maximum principle and prevents non-physical spurious oscillations. Furthermore, we show some numerical experiments in agreement with the previous theoretical results. Finally, numerical comparisons with other schemes found in the literature are also carried out.