Table of Contents
The available Navier-Stokes solvers are all based on a pseudo-spectral space discretization of the equation based on the vorticity formulation. Time is discretized explicitly using a low-storage 3rd order Runge-Kutta scheme.
Three Navier-Stokes solvers are available at the moment:
The second solver for bounded domains treats the penalization term exactly by advancing the solution in physical space instead of Fourier space. Unfortunately this can be done only in the absence of a viscous term. In all cases the nonlinear term is explicit.
A new solver based on active penalization is currently in early development and not documented yet.
A large suite of diagnostic tools come with the Navier-Stokes solver.
| Workspace | Name | Influential parameter(s) | Data type | Description | External dependency |
| fourier | enstrophy | tenstrophy | scalar float | total flow enstrophy (without 1/2 factor) | HDF5 |
| energy | tenergy | scalar float | total flow energy (without 1/2 factor) | HDF5 | |
| palinstrophy | tpalinstrophy | scalar float | total flow palinstrophy (without 1/2 factor) | HDF5 | |
| enstrophy_derivative | tdZdt, nreplics, replic_timestep | scalar float | time derivative of enstrophy | HDF5 | |
| energy_derivative | tdEdt, nreplics, replic_timestep | scalar float | time derivative of energy | HDF5 | |
| fluid_palinstrophy | tfluidpalinstrophy | scalar float | total flow enstrophy (without 1/2 factor) | HDF5 | |
| vorticity_spectrum | tspectrum | 1D float array | flow enstrophy spectrum (non normalized) | HDF5 | |
| grid | vorticity plot | tmovie, palette, resolution | image | color representation of vorticity | VTK |
| pressure plot | tpressure, pressure_palette, resolution | image | color representation of pressure | VTK | |
| vorticity_histogram ("pdf") | thisto | 1d size_t array | histogram of vorticity obtained by binning all the values | HDF5 | |
| vorticity_minimum | tmin | scalar float | minimum value attained by vorticity | HDF5 | |
| vorticity_maximum | tmax | scalar float | maximum value attained by vorticity | HDF5 | |
| vorticity | tsave | 2D float array | complete vorticity field at a given time | HDF5 | |
| vorticity_radial_average | tradial | 1D float array | vorticity averaged along circles centered in the middle of the domain | HDF5 | |
| vorticity_vertical_average | tvertical | 1D float array | vorticity averaged along vertical lines | HDF5 | |
| wavelets | vorticity_tilde | tsave | 2D float array | complete set of wavelet coefficients | HDF5 |
| vorticity_tilde_histogram | thisto | 1D size_t array | histogram of the wavelet coefficients of vorticity | VTK | |
| vorticity_tilde_minimum | tmin | scalar float | minimum value attained by the wavelet coefficients of vorticity | HDF5 | |
| vorticity_tilde_maximum | tmax | scalar float | maximum value attained by the wavelet coefficients of vorticity | HDF5 | |
| scale_dependent_flatness | tsdf | 1D array of 3 component float vectors | statistical flatness of the wavelet coefficients for each scale and direction | HDF5 | |
| vorticity_Jminus2_histogram | tsdpdf | 1D float array | histogram of the wavelet coefficients of vorticity at scale J-2 | HDF5 | |
| vorticity_Jminus2_minimum | tsdpdf | scalar float | minimum value attained by the wavelet coefficients of vorticity at scale J-2 | HDF5 | |
| vorticity_Jminus2_maximum | tsdpdf | scalar float | maximum value attained by the wavelet coefficients of vorticity at scale J-2 | HDF5 | |
| sbs_incoherent_l2 | quantile,sbs_thresholding, max_iter, penalized_fraction | 1D array of 3 component float vectors | incoherent enstrophy in each scale and direction | HDF5 | |
| sbs_coherent_l0 | quantile, sbs_thresholding, max_iter, penalized_fraction | 1D array of 3 component size_t vectors | number of coherent coefficients in each scale and direction | HDF5 | |
| sbs_iterations | quantile, sbs_thresholding, max_iter, penalized_fraction | 1D array of 3 component size_t vectors | number of iterations required for each scale and direction | HDF5 | |
| coherent_l0 | quantile, sbs_thresholding, max_iter, penalized_fraction | scalar size_t | total number of coherent coefficients | HDF5 | |
| incoherent_l2 | quantile,sbs_thresholding, max_iter, penalized_fraction | scalar float | total incoherent enstrophy | HDF5 | |
| vorticity tilde plot | tmovie | image | color representation of the horizontal wavelet coefficients of vorticity at scale J-2 | VTK | |
| wavelets.coherent | all grid diagnostics | analyze_coherent | applies grid diagnostics to the reconstructed coherent part | ||
| wavelets.incoherent | all grid diagnostics | analyze_incoherent | applies grid diagnostics to the reconstructed incoherent part |
All the parameters beginning with the letter 't' indicate the frequency All the diagnostics in Fourier space
The three solvers can be build respectively using the following command line instructions: