Machine Learning Flux-Limiters for Compressible Flow Simulations

The Euler equations governing inviscid compressible flow have a rich history of research devoted to solving them numerically. The main difficulty lays in the potential for singularities caused by shocks forming within the flow field, which necessitate the use of low-order numerical schemes to avoid introducing large, erroneous oscillations into the solution. A popular approach for circumventing this oscillation problem is the use of flux-limiters, which aim to mix low-order and high-order flux representations such that no oscillations are generated near shocks, while high-order accuracy is maintained in smooth regions of the flow. Over the last several decades, numerous flux-limiter schemes have been proposed, largely by varying the mixing function that changes with the local solution smoothness. Here, we propose using a machine-learned flux-limiter to blend low-order and high-order fluxes. The resulting flux-limiter is then applied across multiple coarse-graining levels derived from higher-resolution solution data. Its effectiveness is assessed across a suite of common one-dimensional test cases and compared against popular flux-limiters, such as min-mod, van Leer, and superbee.

This abstract is approved for release under LA-UR-22-27187.