A Data-Driven Reconstruction for Unstructured Finite Volume Method on Multi-Dimensional Compressible Flows (Communications in Computational Physics, 2024)
This paper introduces a novel data-driven shock-capturing for unstructuredfinite volume method (FVM) on multi-dimensional compressible flows, aiming at enhancing accuracy in smooth region while ensuring robustness in discontinuous region,by machine-learning models. We achieve this objective via a two-step process basedon a tree model and fully-connected neural network (FCNN) models. In the first step,a tree model is employed as a troubled-cell indicator to divide the computational domain into discontinuous and smooth regions. In the second step, we employ FCNNmodels to reconstruct solution variables at a cell interface, which are used to obtainnumerical fluxes. Notably, two FCNN models are used for discontinuous and smoothregions, respectively, with the former designed for robust capturing of discontinuities,and the latter intended to enhance accuracy in smooth region. To train such models,we generate two types of datasets using various analytic functions to mimic discontinuous and smooth FVM solutions. In addition, we define specific input features to provide the information on solution distribution and coordinates, enabling the extensiononto unstructured meshes. Finally, we systematically validate the proposed methodthrough a comprehensive set of numerical experiments, ranging from scalar conservation laws, Euler equations to Navier-Stokes equations. Computational experimentsdemonstrate enhanced performance in terms of robustness and accuracy, highlightingthe capability of data-driven reconstruction in complex flow simulations.
Keywords: Finite volume method (FVM); shock-capturing method; data-driven reconstruction method; machine learning (ML); tree model; fully-connected neural network (FCNN).