No abstract

No abstract

No abstract

With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized Unet architecture, and evaluate a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distributions. In particular, we illustrate how training data size and the number of weights influence the accuracy of the solutions. With our best models we arrive at a mean relative pressure and velocity error of less than 3% across a range of previously unseen airfoil shapes. In addition all source code is publicly available in order to ensure reproducibility and to provide a starting point for researchers interested in deep learning methods for physics problems. While this work focuses on RANS solutions, the neural network architecture and learning setup are very generic, and applicable to a wide range of PDE boundary value problems on Cartesian grids.

No abstract

No abstract

No abstract

In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to negative density and pressure, and then imposes a cut-off flux limiter to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory base scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.