FluxNet: Accelerating flux calculation via coarse-to-fine neural modeling

The finite volume method (FVM) has emerged as a dominant numerical framework in computational fluid dynamics for simulating complex flow phenomena, such as aerospace external aerodynamics and internal combustion engine combustion, owing to its exceptional geometric adaptability and numerical stability. Flux calculation as the core component of FVM, directly dictates the performance of large-scale simulations. However, traditional flux splitting schemes, like AUSMPW+ (advection upstream splitting method with pressure-weighted improvements, a classic upwind scheme), suffer from limited computational efficiency on high-resolution grids due to extensive conditional branching and data dependencies. To address this, we introduce FluxNet, an end-to-end flux calculation accelerator based on a lightweight neural network, designed to overcome the bottlenecks of conventional numerical methods. FluxNet employs a coarse sampling-fine prediction framework, where training data are generated on coarse grids to constrain input parameter ranges and reduce data outliers. To ensure physical consistency, this is coupled with an error-guided progressive iterative sampling method, which suppresses error accumulation through dynamic error feedback during iterative computations, ensuring physical consistency. We conduct numerical experiments on canonical test cases, including both one-dimensional and three-dimensional scenarios. The results demonstrate that FluxNet achieves a nearly fourfold acceleration compared to AUSMPW+ while maintaining an average relative error below 0.615%—and its mean absolute percentage error is less than 1%, satisfying engineering-grade accuracy requirements. This study presents a data-driven paradigm for efficient flux calculation in FVM, with potential for multi-scale modeling to expand its applicability to complex engineering scenarios.