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Computational study demonstrates exact energy conservation and entropy stability in coupled phase-field systems, highlighting a robust finite element scheme.
This work presents a conforming finite‐element scheme for non‐isothermal phase‐field systems coupled to the incompressible Navier–Stokes equations. The proposed numerical scheme preserves entropy production and total energy conservation exactly by variable transformations using entropy as the main variable instead of temperature. Convergence tests in space are conducted, and representative examples are provided to demonstrate the scheme's effectiveness.
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Brunk et al. (2026) studied this question.
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