Structure-preserving approximation for non-isothermal phase-field models in melt flow
This work provides a structure-preserving numerical method for complex multiphysics melt flow problems, but it is an incremental extension of existing finite-element techniques.
The authors developed a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system that exactly preserves entropy production and conserves total energy up to negative numerical dissipation, with convergence tests and examples demonstrating effectiveness.
This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The system comprises the incompressible Navier-Stokes equations coupled with the non-isothermal Allen-Cahn equation, which includes a non-conserved phase-field equation and a temperature equation. The proposed numerical scheme preserves entropy production exactly and maintains total energy conservation up to a negative numerical dissipation. Convergence tests in both space and time are conducted, and representative examples are provided to demonstrate the scheme's effectiveness.