Quantifying Numerical Impact of Hanging-Node Interfaces on Flow Accuracy

High-fidelity compressible computational fluid dynamics (CFD) benefits from using hexahedral meshes that are well aligned with the dominant gradients. However, recent advancements in mesh generation offer hanging nodes as a means for local refinement. Previous work using the Modified Steger-Warming (MSW) method reported significant errors when applied to realistic geometries with viscous effects. We reference MSW here to illustrate that its inherent diffusion masks the effects of interfaces, making MSW unsuitable for quantitative error analysis. To quantify the effects of these interfaces on accuracy, we employed a set of low-dissipation, kinetic-energy-consistent (KEC) finite-volume schemes: a baseline second-order formulation together with formally fourth- and sixth-order extensions constructed using weighted least-squares gradients on predominantly structured meshes. We investigated three canonical problems that reveal complementary sensitivities: inviscid and viscous Taylor-Green vortices (TGV) to diagnose error accumulation in smooth vortical fields through normed solution differences and total kinetic energy (KE) decay, and the standing oblique shock to evaluate shock-capturing behavior and entropy production. On uniform meshes, the higher-order KEC schemes perform very similarly to the second-order formulation. On hanging-node meshes, however, their stronger dependence on gradients makes them less robust, with fourth-order KEC becoming unstable and sixth-order KEC remaining accurate for an extended time before ultimately blowing up as interface-generated gradient errors accumulate. In our analysis, misaligned interfaces produced localized defects that convected and accumulated, leading to accelerated kinetic-energy decay and vortex breakdown in the TGV cases, and to entropy streaks where an oblique shock crossed refinement boundaries in the standing oblique shock case. These findings support meshing strategies that maintain hexahedral topology and position refinement interfaces parallel to shocks and principal gradients, and they encourage the development of interface-aware numerical methods such as higher-order face quadrature/reconstruction on nonconformal faces to mitigate error when perfect alignment is not feasible.