scholarly journals Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities

2018 ◽  
Vol 40 (1) ◽  
pp. B138-B167 ◽  
Author(s):  
Yuezheng Gong ◽  
Jia Zhao ◽  
Xiaogang Yang ◽  
Qi Wang
Author(s):  
Eric W. Hester ◽  
Louis-Alexandre Couston ◽  
Benjamin Favier ◽  
Keaton J. Burns ◽  
Geoffrey M. Vasil

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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