Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
This work addresses accuracy issues in computational fluid dynamics simulations for researchers and engineers, representing an incremental improvement over existing deep learning-based methods.
The paper tackles the problem of improving accuracy in numerical simulations of two-dimensional hyperbolic conservation laws, particularly near shocks, by introducing a deep learning-enhanced WENO scheme that outperforms traditional methods in test cases involving shocks and rarefaction waves.
In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a compact neural network to adjust the smoothness indicators within the WENO scheme. This modification enhances the accuracy of the numerical results, particularly near abrupt shocks. Unlike previous deep learning-based methods, no additional post-processing steps are necessary for maintaining consistency. We demonstrate the superiority of our new approach using several examples from the literature for the two-dimensional Euler equations of gas dynamics. Through intensive study of these test problems, which involve various shocks and rarefaction waves, the new technique is shown to outperform traditional fifth-order WENO schemes, especially in cases where the numerical solutions exhibit excessive diffusion or overshoot around shocks.