A Six-Point Shock-Capturing Scheme With Neural Network

A recent study of low-dissipation shock-capturing scheme [Fu et al., Journal of Computational Physics 305 (2016): 333-359] proposed a nonlinear sharp selection function to remove the contributions of candidate stencils containing discontinuities from the final reconstruction. In this paper, we train a neural network to replace this empirical level nonlinear selection function in the six-order TENO6-opt scheme. The performance and robustness of the neuron-based six-point scheme are demonstrated with the advection function and 1D Euler equations.