ABSTRACT Phase-field methods are widely used to model microstructural evolution in complex multiphase systems, including dendrite motion, collision, and coalescence [1]. In an Eulerian setting, however, accurately transporting steep diffuse interfaces remains a major challenge: direct advection typically introduces numerical diffusion and shape distortion that accumulate over time, even with advanced high-order or flux-limited schemes [2]. This progressive smearing undermines the physically correct, shape-preserving motion expected for rigid or nearly rigid solids transported by a flow. We propose a forward–backward mapping framework that avoids direct interface advection by adopt- ing the reference-map strategy of Daubner et al [2] as the core kinematic representation. Instead, we transport smooth mapping fields and reconstruct the evolving phase fields from a stored reference con- figuration, converting the dominant error source from cumulative interface diffusion into a largely time- independent interpolation. Building on this, we introduce a coupled flow–microstructure model for mul- tiple immersed rigid bodies represented by distinct phase fields and interacting with an incompressible Navier–Stokes solver via constraint/forcing terms. Collision and post-collision kinematics are handled in a mapping-consistent way inspired by perfectly inelastic coalescence ideas [1]: overlapping clusters are treated transiently as composite rigid bodies, while phase identities are preserved through projection back onto the original variables. Finally, the framework supports two-way multiphysics coupling by ad- vecting Eulerian driving fields (e.g., temperature) in the current configuration and mapping them into the reference frame to drive microstructural evolution. This yields a robust, collision-capable, and extensible Eulerian platform for flow-driven phase-field simulations. REFERENCES [1] T. Takaki et al., Phase-field lattice Boltzmann modeling of multiple dendrite growth with mo- tion, collision, coalescence, and subsequent grain growth, Computational Materials Science 147, pp. 124–131 (2018). [2] S. Daubner, M. Reder, N. Prajapati, D. Schneider, and B. Nestler, Multiphase-field modelling of anisotropic elasticity at finite deformation in Eulerian space, Journal of Computational Science 66, 101930 (2023). doi:10.1016/j.jocs.2022.101930