An Improved Conservative Hybrid Method with Adaptive Mesh Refinement for Passive-Scalar Transport on Deforming Interfaces

This paper presents an improved hybrid Eulerian–Lagrangian framework, which has been augmented with an adaptive mesh refinement technique, for simulating passive scalar transport on deforming interfaces. We capture interface deformation using an Eulerian level-set method while solving the interfacial transport equation with a single-layer smoothed particle hydrodynamics method. As a result, the proposed hybrid approach combines the high efficiency of the Eulerian formulation with the strict mass conservation property of smoothed particle hydrodynamics method. To further accelerate the simulations, we employ adaptive mesh refinement for the Eulerian solver and restrict particles to the finest refinement level. To mitigate Lagrangian particle clustering, we adopt a remeshing procedure that generates particle distributions adapted to the local interface geometry on the finest mesh. This remeshing also enables accurate, mass-conservative reconstruction of the interfacial concentration field. Moreover, by incorporating an adaptive remeshing strategy, we tune the remeshing frequency to balance computational cost and accuracy. The accuracy and robustness of the proposed method are demonstrated through a suite of benchmark test cases. Additionally, we evaluate the effectiveness of adaptive mesh refinement through benchmark test cases, verifying its compatibility with the interfacial smoothed particle hydrodynamics method and quantifying the resulting speedup.