Computational modeling of incompressible two-phase fluid dynamics via the conservative Allen-Cahn framework on a virtual cube

초록

We present a robust computational algorithm for the simulation of incompressible two-phase fluid flows on a virtual cubic surface, i.e., the models of incorporating the conservative Allen-Cahn (CAC) equation into the Navier-Stokes (NS) equation. By using a phase-field approach, the proposed method effectively captures the evolution of complex interfaces among distinct fluid phases instead of explicit interface tracking. The projection method is combined with the finite difference method (FDM) to solve the governing equations in an efficient manner. In addition, a multigrid solver is adopted to handle the pressure Poisson equation, which improves computational accuracy and reduces computational cost. The virtual cubic surface is modeled as a two-dimensional unfolded domain to facilitate straightforward discretization while preserving geometric fidelity. Numerical experiments, including benchmark shear flow and vortex dynamics on the cubic surface, back up the efficacy of the method in handling two-phase flows. The computational results validate that the proposed scheme has significant potential to advance the simulation of multiphase incompressible flows on curved or complex surfaces. This approach provides an effective numerical method applicable to various scientific and engineering problems.

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