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

Area of Science:

• Computational fluid dynamics
• Materials science
• Phase-field modeling

Background:

• Standard phase-field models offer simplified computation for phase-change problems but suffer from first-order accuracy.
• This inaccuracy leads to errors proportional to the diffuse interface thickness, limiting simulation precision.
• Accurate simulation of melting and dissolution in multi-component flows is crucial for various engineering applications.

Purpose of the Study:

• To develop and analyze the first second-order accurate phase-field model that combines melting and dissolution.
• To provide a computationally simple and accurate method for simulating challenging phase-change phenomena.
• To establish a general framework for asymptotic analysis of diffuse-interface methods.

Main Methods:

• Development of a second-order accurate phase-field model integrating melting and dissolution.
• Application of a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries.
• Validation of the model's second-order convergence using two benchmark problems with the Dedalus spectral code.

Main Results:

• The developed model achieves second-order accuracy, significantly reducing errors associated with diffuse interfaces.
• The framework unifies previous second-order models for melting/dissolution and fluid-solid interaction.
• Successful validation in benchmark problems confirms the model's accuracy and robustness.

Conclusions:

• The novel second-order phase-field model offers a significant advancement for simulating multi-component phase-change flows.
• This approach simplifies complex simulations while maintaining high accuracy, applicable to existing computational codes.
• The established framework provides a pathway for developing more accurate diffuse-interface methods.