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arXiv · 2610.27906

DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver

Pietro Carlo Boldini·Yifu Chen·Marios Kotsonis
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Abstract

We present DeHNSSo-v2, a major update of DeHNSSo-v1 (Westerbeek et al., Comput. Phys. Commun. 302, 2024), the open-source Delft Harmonic Navier-Stokes Solver for nonlinear stability analysis of shear flows. The new release adds a compressible formulation on general two-dimensional body-fitted geometries, automatic grid generation, linear-cost sparse assembly, reusable per-mode factorizations, and Newton pseudo-arclength continuation for high-amplitude nonlinear solutions. The curvilinear formulation preserves the fourth-order accuracy of the discretization on strongly distorted grids, and the compressible solver is confirmed to reproduce DeHNSSo-v1 in the incompressible limit. Validation spans published benchmarks for linear instability of compressible flat-plate boundary layers from $\mathrm{Ma}=0.5$ to $\mathrm{Ma}=4.5$, nonlinear oblique-mode breakdown at $\mathrm{Ma}=1.6$, nonlinear swept-wing crossflow compared with direct numerical simulations, and linear Tollmien-Schlichting wave interaction with a modeled surface-embedded Helmholtz resonator compared with experimentally validated linearized Navier-Stokes simulations. On the nonlinear test cases of DeHNSSo-v1, the computational developments result in a speed-up of approximately one order of magnitude. By broadening the scope and reducing the cost of DeHNSSo-v1, DeHNSSo-v2 provides the boundary-layer-transition and flow-control community with an accessible tool for studying receptivity, nonlinear disturbance evolution, and instability interactions with complex surface geometry and metamaterials across compressibility regimes.

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Pietro Carlo Boldini, Yifu Chen, Marios Kotsonis. 2026-10-20. DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver. https://arxiv.org/abs/2610.27906

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