2026-10-06T07:28:49Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33897235 2026-09-17T14:45:08Z category_29812 category_26590 category_29779 category_29821 item_type_3 month_year_09_2026

Supplementary Material and Reproducibility Archive for Variable-mass consistency for high-order transient source-corrected compact finite differences on nonuniform grids Tingfu Ma (24977770) Zhenghang Wang (24973096) Baiying Dong (24978575) Yongbin Ge (24978590) Numerical analysis Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics) Applied mathematics not elsewhere classified Numerical and computational mathematics not elsewhere classified source-corrected compact difference variable mass operator nonuniform grid convection-diffusion compact finite difference backward differentiation formula BDF Radau-IIA Schur complement GMRES numerical analysis reproducibility <p dir="ltr">This dataset and supplementary material accompany the manuscript “Variable-mass consistency for high-order transient source-corrected compact finite differences on nonuniform grids.”</p><p><br></p><p dir="ltr">The study develops a variable-mass consistency principle for transient source-corrected compact finite-difference discretizations on nonuniform Cartesian grids. For the blended compact difference (BCD) method, the formulation consistently incorporates the drift-dependent mass operator into current-mass BDF2, BDF5, and BDF6 time integration, together with a three-stage fifth-order Radau-IIA startup procedure, exact Schur elimination of derivative fields, matrix-free Krylov solution, and high-order treatment of Dirichlet, Neumann, and Robin boundary conditions. The accompanying numerical experiments examine spatial and temporal convergence, mesh-stretching robustness, mixed-boundary accuracy, stability behavior, and Schur-solver performance.</p><p><br></p><p dir="ltr">The supplementary package provides the complete BCD coefficient specification, algebraic and symbolic verification details, auxiliary numerical results, and additional verification figures. The reproducibility archive contains executable verification code, machine-readable numerical tables, reference-calculation outputs, automated tests, plotting scripts, and related files supporting reproduction and independent checking of the principal theoretical and numerical results reported in the manuscript.</p> 2026-09-17T14:45:08Z Dataset Dataset 10.6084/m9.figshare.33897235.v1 https://figshare.com/articles/dataset/Supplementary_Material_and_Reproducibility_Archive_for_Variable-mass_consistency_for_high-order_transient_source-corrected_compact_finite_differences_on_nonuniform_grids/33897235 CC BY 4.0