Nonlinear constitutive calculation method of rarefied flow based on deep convolution neural networks

Abstract

In the field of rarefied gas dynamics, the presence of non-equilibrium flow characteristics poses significant challenges for achieving efficient and accurate numerical simulation methods. These challenges arise from the complex coexistence of these phenomena at multiple scales. The recent advent of intelligent fluid mechanics has introduced the data-driven nonlinear constitutive relation (DNCR) method as a promising approach for expeditious physical modeling of non-equilibrium rarefied flows. To enhance the generalization capabilities of the DNCR method, this study proposes a deep convolutional neural network model (DNCR-CNN) based on data-driven nonlinear constitutive relations, integrated with free-form deformation (FFD). Employing FFD technology, a series of hypersonic geometric shapes are generated for model training, and a multi-task learning-based deep convolutional neural network model is subsequently trained. The prediction of the hypersonic geometric shapes test set is carried out, and the results of the model prediction are substituted in the conservation equation for the iterative solution, thereby enhancing the DNCR method's generalization performance for varying geometric shapes. Upon conducting a comparative analysis of the outcomes obtained from DNCR, Navier–Stokes (NS), and unified gas kinetic scheme (UGKS), it is revealed that the DNCR method can maintain computational resource levels equivalent to those of the NS equation while achieving a level of accuracy comparable to UGKS under diverse geometric shapes and grid resolutions. The enhancements in usability render the DNCR method a potent tool for addressing the challenges posed by rarefied gas, thereby expanding its applicability within the field.