Improved phase-field models of melting and dissolution in multi-component flows

TL;DR

This paper introduces a second-order phase-field model that accurately simulates melting and dissolution in multi-component flows, improving computational efficiency and precision over traditional first-order models.

Contribution

The authors develop a unified second-order phase-field framework for melting and dissolution, validated through comprehensive benchmarks, advancing phase-change simulation accuracy.

Findings

Achieved second-order convergence in benchmark tests

Unified previous models and volume-penalty method

Validated with open-source spectral code Dedalus

Abstract

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretisations that track the moving phase boundary. However standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.