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Updated: Dec 24, 2025
07:28
Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
6.8K
Thin interface limit of the double-sided phase-field model with convection
Amol Subhedar1, Peter K Galenko2,3, Fathollah Varnik4
1Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestr. 30, 76133 Karlsruhe, Germany.
Summary
This study extends the phase-field model to include melt convection, comparing two coupling schemes for simulations. Both methods show similar results for dendritic growth with melt flow, validating their use in simulations.
Area of Science:
- Computational physics
- Materials science
- Fluid dynamics
Background:
- Phase-field models are crucial for simulating material microstructures.
- Incorporating melt convection is essential for accurate predictions in many processes.
- Understanding the interplay between phase-field dynamics and fluid flow is key.
Purpose of the Study:
- To extend the thin interface limit of phase-field models to include melt convection.
- To investigate and compare two schemes for coupling phase-field and Navier-Stokes equations.
- To analyze the impact of melt flow on dendritic growth profiles.
Main Methods:
- Matched asymptotic analysis to investigate coupling schemes.
- Development of a double-sided phase-field model with equal diffusivity.
- Two-dimensional numerical simulations of dendritic growth under forced melt flow.
Main Results:
- The variable viscosity model allows for a thin interface limit up to the second order.
- Difficulties were encountered with the drag force model's no-slip boundary condition at the second order.
- Numerical simulations showed negligible differences in dendritic growth between the two schemes with forced melt flow.
Conclusions:
- Both variable viscosity and drag force models are suitable for numerical simulations of phase-field with melt convection.
- Simulation results align well with analytic theory for weak fluid flow.
- Deviations at higher flow rates are attributed to underlying theoretical assumptions.
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