Improving the Robustness and Applicability of Higher-accuracy EBR Schemes

The Edge-Based Reconstruction (EBR) schemes are designed to provide higher-accuracy approximation of convective terms of the Navier–Stokes Equations on conformal unstructured mixed-element meshes. The target application area is high-fidelity scale-resolving simulations of compressible turbulent flows. These schemes are computationally inexpensive and have relatively low memory consumption due to the use of quasi-1D interpolation constructions along mesh edges. On translation-invariant meshes, such schemes reach up to 5th order accuracy with two-level interpolation constructions. However, apart from these obvious advantages, the EBR schemes also have some significant drawbacks. These schemes can be very capricious in practice and overly sensitive to mesh quality. For instance, large differences in segment lengths in interpolation constructs can cause many problems, such as significant accuracy drops, unstable behavior, unphysical perturbations, and even simulation crash. This is not the behavior one would expect from a high-accuracy scheme intended for practical use. Therefore, the present article proposes a rather simple remedy that heals this problem and makes the EBR schemes much more robust.