Numerical dataset for "A Tensor Constitutive Framework for Adaptive Momentum Redistribution in Incompressible Flow"

This dataset accompanies the manuscript “A Tensor Constitutive Framework for Adaptive Momentum Redistribution in Incompressible Flow.” It contains numerical results from three-dimensional Taylor–Green vortex simulations of the incompressible Navier–Stokes equations and the tensor Directional Momentum Redistribution, or tensor DMR, model in the periodic domain from 0 to 2 pi in each spatial direction. In the tensor DMR formulation, the velocity field is coupled to an independently transported, symmetric, trace-free redistribution-stress tensor. The tensor evolves through advection, corotational rotation, production by the strain-rate tensor, diffusion, and strain-dependent relaxation. The relaxation rate is defined as c0 plus c1 multiplied by the square of the strain-rate magnitude. The dataset includes: the complete N equals 64 Navier–Stokes reference simulation; tensor DMR simulations at N equals 64 for c1 equal to 0, 0.05, 0.10, and 0.20; an N equals 64 timestep-refinement run using a timestep of 0.0005; matched N equals 128 Navier–Stokes and tensor DMR simulations; time histories of kinetic energy, tensor energy, and total energy; enstrophy and vortex-stretching diagnostics; velocity-to-tensor energy-transfer data; viscous, tensor-diffusion, baseline-relaxation, and strain-activated-relaxation dissipation components; kinetic-energy spectra; final three-dimensional fields; three-dimensional fields at the time of peak vortex stretching; localization statistics for the strain-activated relaxation density; validation results for the coupled total-energy and tensor-energy identities; solver code, Colab notebooks, publication figures, tables, and LaTeX source files. For the matched N equals 128 simulations, using a timestep of 0.001 and a final simulation time of 4, the peak vortex-stretching functional decreases from 32.24892493 in the Navier–Stokes simulation to 18.30384720 in the tensor DMR simulation. This corresponds to a reduction of approximately 43.24 percent. The strain-activated relaxation is strongly localized. In the representative c1 equals 0.10 case, the correlation between the local strain-activated relaxation density and the strain intensity is approximately 0.906 at the time of peak vortex stretching. Approximately 50 percent of the total strain-activated relaxation is concentrated within only 4.93 percent of the computational volume. The numerical implementation reproduces the analytical energy structure to high accuracy. For the N equals 128 tensor simulation, the maximum relative total-energy residual is approximately 9.60 times 10 to the minus 8, and the maximum relative tensor-energy residual is approximately 4.26 times 10 to the minus 7. The divergence error, tensor-trace error, and spectral Parseval errors remain close to machine precision. The spectral results indicate a non-uniform redistribution of kinetic energy across scales. The tensor model reduces the dominant low-to-intermediate wavenumber energy, while a crossover occurs in the very small-energy high-wavenumber tail. The model should therefore be interpreted as a transported constitutive redistribution mechanism rather than as a uniform spectral filter or a conventional eddy-viscosity model. The Zenodo record contains the following files: Tensor_DMR_Taylor_Green_Dataset_v1.0.0.zip N128_NS.zip N128_tensor_c1_0p10.zip The data, figures, and documentation are released under the Creative Commons Attribution 4.0 International licence. The solver code and notebooks are additionally released under the BSD 3-Clause Licence.