Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operator

This paper builds up a virtual domain extension (VDE) framework for imposing boundary conditions (BCs) in flow simulation using pre-trained local neural operator (LNO). It creates extended virtual domains to the input function to compensate for the corrosion nature of computational domains during LNO inference, thus turns the implementation of BC into the determination of field values on the extended domain. Several strategies to calculate the field values are proposed and validated in solving numerical examples, including padding operation, direct imposition, pressure symmetry, and optimization by backpropagation, and compared with boundary imposition in traditional solvers. It is found that the large time interval of LNO induces a relatively wide near-boundary domain to be processed, thus imposing BC on only a few nodes near the boundary following the immersed boundary conception in traditional solvers can hardly achieve high accuracy. With appropriate values assigned on the extended virtual domains, VDE can accurately impose BCs and lead to reasonable flow field predictions. This work provides a guidance for imposing BCs reliably in LNO prediction, which could facilitate the reuse of pre-trained LNO in more applications.