DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver
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 Ma=0.5 to Ma=4.5, nonlinear oblique-mode breakdown at 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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BibTeX
@misc{boldini2026dehnssov2,
title = {{DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver}},
author = {Pietro Carlo Boldini and Yifu Chen and Marios Kotsonis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27906},
eprint = {2610.27906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27906},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver
AU - Pietro Carlo Boldini
AU - Yifu Chen
AU - Marios Kotsonis
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27906
UR - https://arxiv.org/abs/2610.27906
AB - 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 Ma=0.5 to Ma=4.5, nonlinear oblique-mode breakdown at 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.
ER -