Data-driven Taylor-Galerkin finite-element scheme for convection problemsDownload PDF

Sep 27, 2021 (edited Dec 05, 2021)DLDE Workshop -- NeurIPS 2021 PosterReaders: Everyone
  • Abstract: High-fidelity large-eddy simulations (LES) of high Reynolds number flows are essential to design low-carbon footprint energy conversion devices. The two-level Taylor-Galerkin (TTGC) finite-element method (FEM) has remained the workhorse of modern industrial-scale combustion LES. In this work, we propose an improved FEM termed ML-TTGC that introduces locally tunable parameters in the TTGC scheme, whose values are provided by a graph neural network (GNN). We show that ML-TTGC outperforms TTGC in solving the convection problem in both irregular and regular meshes over a wide-range of initial conditions. We train the GNN using parameter values that (i) minimize a weighted loss function of the dispersion and dissipation error and (ii) enforce them to be numerically stable. As a result no additional ad-hoc dissipation is necessary for numerical stability or to damp spurious waves amortizing the additional cost of running the GNN.
  • Publication Status: This work is unpublished.
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