Physics foundation models are becoming a popular way to build versatile emulators for spatiotemporal systems. These models require a tokenisation layer that lifts physical field data into a latent representation suitable for dynamic processing. The typical choice is a convolutional encoder (CNN), which extracts local information efficiently and can be trained quickly.\ However, when data are stored on unstructured meshes—e.g., domains with curved boundaries—CNNs cannot be applied directly. Graph neural networks (GNNs) are usually employed, but they are more expensive to train and encode information differently from CNNs, limiting the portability of physics emulators across data regimes.\ We introduce Mesh‑Native Convolution (MNC), a locality‑aware tokenisation layer that encodes unstructured mesh data in a manner analogous to CNNs. MNC performs convolution over the mesh adjacency, providing a unified representation for irregular meshes. Consequently, a model trained once on a particular mesh can be deployed to arbitrary unstructured meshes with minimal retraining.\ Theoretical analysis shows that, in the fine‑grid limit, MNC converges to the classical CNN encoder, guaranteeing consistency. Empirical results demonstrate that retrofitting a grid‑pretrained foundation model with MNC yields acceptable accuracy in zero‑shot deployment and surpasses existing baselines after only a few fine‑tuning epochs. This approach offers an efficient bridge between structured and unstructured data regimes.\ \ Review: MNC preserves the locality of convolution while addressing the tokenisation challenge of unstructured meshes, providing a practical pathway for cross‑domain transfer of physics models.