Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models

2011 ◽  
Vol 230 (13) ◽  
pp. 5310-5327 ◽  
Author(s):  
Hector Gomez ◽  
Thomas J.R. Hughes
Keyword(s):  
Variational Methods ◽  
Phase Field ◽  
Second Order ◽  
Unconditionally Stable ◽  
Phase Field Models

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

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200508
Author(s):  
Eric W. Hester ◽  
Louis-Alexandre Couston ◽  
Benjamin Favier ◽  
Keaton J. Burns ◽  
Geoffrey M. Vasil
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Second Order ◽  
Diffuse Interface ◽  
Benchmark Problems ◽  
First Order ◽  
Phase Field Models ◽  
Arbitrary Geometries ◽  
Second Order Convergence ◽  
Fluid Solid Interaction

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.

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