A deep learning approach for adaptive zoning
This work addresses computational efficiency in shock wave simulations for researchers in computational fluid dynamics, but it is incremental as it applies existing deep learning methods to a known bottleneck in adaptive zoning.
The paper tackles the problem of adaptive zoning for 1D shock wave simulations by proposing a supervised deep learning model that learns to generate adapted meshes from static shock profiles, reducing computational time by at least 2x compared to standard techniques while maintaining accuracy.
We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset composed of different static shock profiles associated with the corresponding adapted meshes computed with standard adaptive zoning techniques. We show that the trained DL model learns how to capture the presence of shocks in the domain and generates at each time step an adapted non-uniform mesh that relocates the grid nodes to improve the accuracy of Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space discretization schemes. We also show that the surrogate DL model reduces the computational time to perform adaptive zoning by at least a 2x factor with respect to standard techniques without compromising the accuracy of the reconstruction of the physical quantities of interest.