International Journal for Numerical Methods in Engineering, Volume 127, Issue 7, 15 April 2026.ABSTRACT In this article, we propose a novel numerical framework for the non‐isothermal Cahn–Hilliard–Navier–Stokes two‐phase flow system, which couples the incompressible Navier–Stokes equations, the Cahn–Hilliard phase‐field equation, and the heat transport equation to capture temperature‐dependent two‐phase flow dynamics.
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