DISSIPAZIONE ARTIFICIALE BASATA SU RETE NEURALE PER APPROSSIMAZIONE DI ORDINE ELEVATO PER LE EQUAZIONI DI EULERO COMPRIMIBILI

Numerical approximation of solutions to the compressible gas dynamics equations with a highorder discontinuous Galerkin method may exhibit discontinuities such as shock and contact waves which make difficult the design of numerical schemes of their approximation. A common approach consists in using artificial dissipation for the improvement of the stability and robustness of the numerical scheme. However, the tuning of the artificial dissipation is usually difficult and might end in lack of damping of spurious oscillations, or and excessive smearing of the discontinuities. The aim of this work is to use neural networks to tune numerical parameters that define the amount of artificial dissipation in an automatic way. The work shows that a neural network based approach guarantees a more accurate solution near discontinuities respect to a constant artificial dissipation approach. A first data assimilation procedure is introduced to provide reference data and the neural network training phase is shown. The neural network has been implemented in the Aghora code, a high-order discontinuous Galerkin solver for Euler equations developed at ONERA, the French Aerospace Lab and numerical tests have been done in order to evaluate the generalization properties of the neural network.