Adaptive numerical dissipation control for high-order k-exact reconstruction schemes on vertex-centered unstructured grids using artificial neural networks

Abstract

Due to their enhanced numerical dissipation properties, high-order discretization methods are an important prerequisite to obtain accurate results with Large-Eddy Simulations. However, the exact amount of dissipation often requires a careful tuning by the user via problem-dependent parameters. In this work we present a fully adaptive dissipation control, which ensures stability and additionally reduces the numerical dissipation to a minimum. This novel approach employs a simple feedforward neural network model, which indirectly tabulates an underlying stability equation and thus reduces the computational overhead to estimate the dissipation during runtime. The methodology is adapted for a high-order k-exact reconstruction method on fully unstructured vertex-centered grids, and it is implemented in a full production flow solver. Based on several test cases, the enhanced accuracy compared to a conventional low-order scheme is demonstrated. Especially when dealing with Large-Eddy Simulation benchmarks, significant savings in computation time and grid resolution requirements can be obtained for reaching a desired level of accuracy. Moreover, compared to a high-order reconstruction method with constant numerical dissipation, the presented adaptive approach consistently yields accurate results, regardless of the flow problem.