High-fidelity flow field reconstruction model for incompressible fluid with physical constraints

Abstract

Research on the flow characteristics of incompressible fluids in the field of ship and ocean engineering is important. The direct numerical simulation method can obtain all information on the flow field by solving the full-scale Navier-Stokes equations. However, it has high computational cost and low computational efficiency. By contrast, the Reynold-averaged Navier-Stokes method has significantly better efficiency and is widely used in engineering, but it is not as accurate as the direct numerical simulation method (DNS). In recent years, deep learning has developed rapidly and provided a new method for the study of fluid flow characteristics. However, current models have many problems in three-dimensional cases, at high Reynolds numbers, and with inverse problem solving. To address these problems, we propose a high-fidelity flow field reconstruction model, namely, HFRIF for incompressible fluids. The method introduces reduced-order differential equation of viscous fluid motion and low-fidelity the Reynold-averaged Navier-Stokes method (RANS) simulation data as constraints in the loss function. We apply it to the reconstruction of two-dimensional and three-dimensional flow fields around a cylinder with Reynolds numbers of 100 and 10000, respectively, and compare it to the high-fidelity flow field data. Finally, super-resolution reconstruction of the flow field and the inversion of physical equation parameters are studied under the same model parameter settings. We find that even in three-dimensional cases and at high Reynolds numbers, the model only needs low-fidelity data to realize high-fidelity flow field reconstruction. Moreover, high-precision super-resolution flow field reconstruction and high-precision parameter inversion can be achieved without changing the model hyper-parameters.