A High-Resolution Finite-Difference Framework for Steady Continuation and Finite-Window Unsteady Dynamics up to Re = 100,000 in 2D Lid-Driven Cavity Flows

Reference CFD Benchmark Suite, 30 Datasets & Research Preprint (v2.0.0) This release provides the complete open-source scientific software suite, 30 verified high-resolution benchmark flow-field datasets, and the full research preprint accompanying the submission to Computers & Fluids (Elsevier): "A High-Resolution Finite-Difference Framework for Steady Continuation and Finite-Window Unsteady Dynamics up to $Re = 100{,}000$ in 2D Lid-Driven Cavity Flows" Author: Kartikey Singh (Department of Mathematics, University of Delhi) Preprint PDF: paper/manuscript.pdf (25 pages, 32 verified references, 4 Appendices) What's Included in this Release? 1. Research Manuscript & Submission Archive paper/manuscript.pdf: Complete 25-page compiled article adhering to Elsevier Computers & Fluids standards with 32 audited references. submission_package/: Ready-to-submit archive containing Cover Letter, Highlights, Manuscript, Declaration of Competing Interest, and Reviewer Nominations. 2. 30 Verified Flow-Field Datasets (data/) All flow fields are serialized as standard NumPy binary archives (.npz) containing coordinate grids (X, Y), streamfunction $\psi$, vorticity $\omega$, velocity fields (u, v), dynamic pressure $p$, and cell Péclet distributions: 23 Stationary Continuation Solutions ($Re = 100 \to 100,000$): $Re = 100, 1{,}000$ on $129 \times 129$ $Re = 3{,}200, 5{,}000, 7{,}500, 10{,}000, 15{,}000, 20{,}000, 25{,}000, 30{,}000$ on $257 \times 257$ $Re = 10{,}000, 15{,}000, 20{,}000, 25{,}000, 30{,}000, 35{,}000, 40{,}000, 45{,}000, 50{,}000, 100{,}000$ on $513 \times 513$ $Re = 100{,}000$ ultra-resolution benchmark on $1025 \times 1025$ ($1{,}050{,}625$ nodes) 7 Finite-Window Unsteady Telemetry Records: $Re = 10{,}000, 15{,}000$ on $257 \times 257$ ($t = 20.0\text{--}22.0$) $Re = 10{,}000, 15{,}000, 25{,}000, 50{,}000, 100{,}000$ on $513 \times 513$ ($t = 16.0\text{--}22.0$) Full cryptographic SHA-256 checksums documented in Appendix A (tab:dataset_manifest). 3. High-Performance CFD Algorithms Fast $\mathcal{O}(N^2 \log N)$ DST-I Poisson Solver: Direct Discrete Sine Transform elliptic solver eliminating iterative algebraic residual drift ($< 4,\text{ms}$ on $513^2$, $< 24,\text{ms}$ on $1025^2$). Vectorized ADI Marching: Slice-parallel directional Thomas algorithm tridiagonal solves in NumPy. Spatial Monotonicity & Hybrid Regularization: Pure second-order central differencing ($\nu_{\text{art}} = 0$) preserved for all $Re \le 50{,}000$; directional hybrid differencing at $Re = 100{,}000$ with full dissipation tensor mapping. ASME V&V 20 Verification: Rigorous Grid Convergence Index (GCI) and Richardson extrapolation. Quick Start: Inspecting Benchmark Data import numpy as np Load high-resolution stationary benchmark at Re = 100,000 on 1025 x 1025 mesh data = np.load("data/flow_fields_Re100000_N1025.npz") X, Y = data["X"], data["Y"] # Coordinate grids psi = data["psi"] # Streamfunction omega = data["omega"] # Vorticity u, v = data["u"], data["v"] # Velocity components print(f"Loaded Re = {data['Re']}, Mesh = {data['N']}x{data['N']}") print(f"Primary Vortex Minimum Streamfunction psi_min = {psi.min():.7f}") Citation If you use this benchmark data or software in your research, please cite: @article{singh2026lid_driven_cavity, title={A High-Resolution Finite-Difference Framework for Steady Continuation and Finite-Window Unsteady Dynamics up to $Re = 100{,}000$ in 2D Lid-Driven Cavity Flows}, author={Singh, Kartikey}, journal={Submitted to Computers \& Fluids}, year={2026} } @misc{singh2026dataset, author = {Singh, Kartikey}, title = {[dataset] Reference Finite-Difference Solutions and Verification Datasets for {2D} Lid-Driven Cavity Flows up to Extreme {Reynolds} Numbers}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.18312938}, url = {https://doi.org/10.5281/zenodo.18312938} }