In recent years, augmentation of PDE solvers with neural networks have shown promising results, particularly in fluid simulations. The general idea is to extend a differentiable numerical solver with learnable components similar to closure models [1]. The augmented solver, running on a coarse grid, is then trained on data from a high-resolution simulation, e.g. direct numerical simulation [1]. With the learned model, a desired accuracy can be achieved using considerably less cells and thus computation time. In contrast to purely data-driven methods where the classical solver is completely replaced (or rather only used to generate the training data), this approach promises much better generalization capabilities. Adding learned components to a solver can be realized in different ways. For instance, [2] introduced an additive correction term and [3] learned interpolation parameters in the advection scheme. However, in both these cases and as in most examples reported in the literature, neural networks are employed that require non-local information to compute their output. In detail, in [2] and [3] Convolutional Neural Networks are used. They leverage the Cartesian grids of the solver, but large computational stencils emerge. Equally, in [4] a Fourier Neural Operator [5] is used, making the learned component fully non-local. While [6] provides one of the rare examples of this type of approach with a solver operating on unstructured meshes, it uses a Graph Neural Network to compute the correction, making the model also non-local. Requiring non-local information in the learned components poses challenges for industrial-grade solvers that operate on unstructured meshes in a highly parallelized way, where efficient access is restricted to neighboring cells, only. In this work, we address this limitation by introducing a novel architecture of the neural nets used in the learned component such that only locally available information is passed to the net. Our results show that our new approach is comparable to, or improves upon, previous methods in terms of pointwise and statistically accuracy and computational efficiency. REFERENCES [1] B. Sanderse, P. Stinis, R. Maulik and S. E. Ahmed. Scientific machine learning for closure models in multiscale problems: A review. arXiv preprint arXiv:2403.02913, 2024 [2] K. Um, R. Brand, Y. R. Fei, P. Holl and N. Thuerey. Solver-in-the-loop: Learning from differentiable physics to interact with iterative pde-solvers. Adva