Diffuse interface treatment in generalized curvilinear coordinates with grid-adapting interface thickness

TL;DR

This paper introduces a transformation method for phase field equations in generalized curvilinear coordinates, enabling accurate, grid-independent interface modeling on complex grids without oscillations.

Contribution

It presents a novel transformation approach that accurately adapts interface thickness to local grid size in curvilinear coordinates, maintaining convergence and robustness.

Findings

The method achieves grid-independent convergence in Rayleigh-Taylor instability simulations.

It extends classic tests to curvilinear grids with consistent order of convergence.

The approach handles complex interfacial structures accurately on various grid types.

Abstract

A general approach for transforming phase field equations into generalized curvilinear coordinates is proposed in this work. The proposed transformation can be applied to isotropic, non-isotropic, and curvilinear grids without adding any ambiguity in determining the phase field parameters. Moreover, it accurately adapts the interface thickness to the local grid-size for a general curvilinear grid without creating oscillations. Three canonical verification tests are presented on four grids with varying skewness levels. The classic advection and drop in shear tests are extended to curvilinear grids and show that the original phase field on Cartesian grids and the proposed curvilinear form have an identical order of convergence. Additionally, the proposed method is shown to provide grid-independent convergence on a two-way coupled compressible Rayleigh-Taylor instability. These simulations illustrate the robustness and accuracy of the proposed method for handling complex interfacial structures on generalized curvilinear grids.