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 discretizations 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.
| Original language | English |
|---|---|
| Article number | 20200508 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 476 |
| Issue number | 2242 |
| Early online date | 21 Oct 2020 |
| DOIs | |
| Publication status | Published - 28 Oct 2020 |
Data Availability Statement
The Dedalus code is free and open-source and available at http://dedalus-project.org/. All simulation code, data and analysis scripts and plots are available at https://github.com/ericwhester/ phase-field-code. The Mathematica asymptotics script is also available at that link.Acknowledgements
E.W.H. project conception and design, writing, mathematics (asymptotics and remapping), simulation code, data analysis and visualization; L.-A.C. project design and conception; B.F. project design and conception, phase-field expertise; K.J.B. domain remapping simulation expertise, Dedalus code; G.M.V. mathematics of signed distance coordinates, Dedalus code. All authors provided critical revision of the manuscript, approve the final version of the paper and agree to be held accountable for the work.We acknowledge PRACE for awarding us access to Marconi HPC at CINECA, Italy, and The University of Sydney for access to the Artemis HPC.
Funding
E.W.H. acknowledges support from The University of Sydney Phillip Hofflin International Research Travel Scholarship, Postgraduate Research Support Scheme and William and Catherine McIlrath Scholarship. L.-A.C. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. MIMOP 793450.
| Funders | Funder number |
|---|---|
| Horizon 2020 Framework Programme | 793450 |
| University of Sydney |
Keywords
- multi-component flows
- phase-field model
- second-order accuracy
ASJC Scopus subject areas
- General Mathematics
- General Engineering
- General Physics and Astronomy