Pseudo-spectral vs. Finite-Difference Solvers
Relative accuracy of numerical schemes for long-time turbulence simulation.
While spectral solvers are theoretically more accurate per timestep, this work demonstrated that pseudo-spectral and finite-difference methods yield nearly identical results for long-term turbulence simulations.
Simulating forced homogeneous turbulence on \(256^3\) grids at Reynolds numbers up to \(\sim 2000\), I compared the pseudo-spectral solver Py-Tarang against the finite-difference solver Py-Saras. Despite higher per-timestep error, the finite-difference solver matched spectral accuracy across energy evolution, spectra, energy flux, and velocity-derivative PDFs.
The central finding: within a turbulence attractor, numerical errors tend to cancel rather than accumulate, supporting the use of more scalable finite-difference solvers for large-grid DNS. Simulations were GPU-accelerated using in-house CuPy frameworks on NVIDIA hardware.