Synopsis

CaNS (Canonical Navier-Stokes) is a code for massively-parallel numerical simulations of fluid flows. It aims at solving any fluid flow of an incompressible, Newtonian fluid that can benefit from a FFT-based solver for the second-order finite-difference Poisson equation in a 3D Cartesian grid. In two directions the grid is regular and the solver supports the following combination of (homogeneous) boundary conditions:

• Neumann-Neumann
• Dirichlet-Dirichlet
• Neumann-Dirichlet
• Periodic

In the third domain direction, the solver is more flexible as it uses Gauss elimination. There the grid can also be non-uniform (e.g. fine at the boundary and coarser in the center).

CaNS also allows for choosing an implicit temporal discretization of the momentum diffusion terms, either fully implicit or only along the last domain direction. This results in solving a 3D/1D Helmholtz equation per velocity component. In the fully implicit case, FFT-based solvers are also used, and the same options described above for pressure boundary conditions apply to the velocity.

Reference

P. Costa. A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows. Computers & Mathematics with Applications 76: 1853--1862 (2018). doi:10.1016/j.camwa.2018.07.034 [arXiv preprint]

News

[10/08/2023]: The input files dns.in and cudecomp.in have been replaced with the namelist file input.nml, which makes parsing of input files and extensions in more complex solvers based on CaNS simpler. See the updated docs/INFO_INPUT.md file for more details. Additionally, we have added a new input parameter, gtype to explicitly select the type of grid stretching function.

[03/02/2023]: The input file dns.in has been simplified to avoid a common source of confusion. Instead of prescribing uref, lref, and rey (reference velocity and length scales, and Reynolds number) to calculate the fluid viscosity as visc = uref*lref/rey, we directly prescribe the inverse of the viscosity, visci (visc = visci**(-1)), so all inputs are dimensional (see the updated docs/INFO_INPUT.md file). Note that visci has the same value as the flow Reynolds number for all files under examples, as uref and lref were always equal to 1. This change is backwards-incompatible - former input files should be updated from v2.2.0 onward!

[24/10/2022]: Option SINGLE_PRECISION_POISSON has been removed from the main branch. While solving the Poisson in lower precision equation yields excellent results for many benchmarks, several of these cases also perform well when the whole calculation is performed in lower precision (see https://github.com/CaNS-World/CaNS/pull/42). Since this mode introduces significant complexity, it will be removed from the main branch for now in favor of a more readable code, a decision that can be reconsidered in the future. This option can still be explored in v2.0.1, and is valuable for, e.g., setups with high Reynolds numbers and/or with extremely fine grids.

Major Update: CaNS 2.0 is finally out! :tada:

CaNS 2.0 has many new features, being the result of the most significant revision effort undertaken so far. It includes major improvements in performance and robustness, and a fresh hardware-adaptive many-GPU parallelization using the cuDecomp library. See docs/CaNS-2.0.md for a detailed description of all new features. CaNS 2.0 has been tested and observed to run efficiently on some major GPU-accelerated clusters such as Perlmutter, Summit, and Marconi 100.

Features

Some features are:

• Hybrid MPI/OpenMP parallelization
• FFTW guru interface / cuFFT used for computing multi-dimensional vectors of 1D transforms
• The right type of transformation (Fourier, cosine, sine, etc) is automatically determined form the input file
• cuDecomp pencil decomposition library for hardware-adaptive distributed memory calculations on many GPUs
• 2DECOMP&FFT library used for performing global data transpositions on CPUs and some of the data I/O
• GPU acceleration using OpenACC directives
• A different canonical flow can be simulated just by changing the input files

Some examples of flows that this code can solve are:

• periodic or developing channel
• periodic or developing square duct
• tri-periodic domain
• lid-driven cavity

Motivation

This project aimed first at being a modern alternative to the well-known FISHPACK routines (Paul Swarztrauber & Roland Sweet, NCAR) for solving a three-dimensional Helmholtz equation. After noticing some works simulating canonical flows with iterative solvers -- when faster direct solvers could have been used instead -- it seemed natural to create a versatile tool and make it available. This code can be used as a first base code for which solvers for more complex flows can be developed (e.g. extensions with fictitious domain methods).

Method

The fluid flow is solved with a second-order finite difference pressure correction scheme, discretized in a MAC grid arrangement. Time is advanced with a three-step low storage Runge-Kutta scheme. Optionally, for increased stability at low Reynolds numbers, at the price of higher computational demand, the diffusion term can be treated implicitly. See the reference above for details.

Usage

Downloading CaNS

Since CaNS loads the external pencil decomposition libraries as Git Submodules, the repository should be cloned as follows:

git clone --recursive https://github.com/CaNS-World/CaNS

so the libraries are downloaded too. Alternatively, in case the repository has already been cloned without the Submodules (i.e., folders cuDecomp and 2decomp-fft under dependencies/ are empty), the following command can be used to update them:

git submodule update --init --recursive

Compilation

Prerequisites

The prerequisites for compiling CaNS are the following:

• MPI
• FFTW3/cuFFT library for CPU/GPU runs
• The nvfortran compiler (for GPU runs)
• NCCL and NVSHMEM (optional, may be exploited by the cuDecomp library)
• OpenMP (optional)

In short

For most systems, CaNS can be compiled from the root directory with the following commands make libs && make, which will compile the 2DECOMP&FFT/cuDecomp libraries, and CaNS.

Detailed instructions

The Makefile in root directory is used to compile the code, and is expected to work out-of-the-box for most systems. The build.conf file in the root directory can be used to choose the Fortran compiler (MPI wrapper), and a few pre-defined profiles depending on the nature of the run (e.g., production vs debugging), and pre-processing options, see INFO_COMPILING.md for more details. Concerning the pre-processing options, the following are available:

• DEBUG : performs some basic checks for debugging purposes
• TIMING : wall-clock time per time step is computed
• IMPDIFF : diffusion terms are integrated implicitly in time (thereby improving the stability of the numerical algorithm for viscous-dominated flows)
• IMPDIFF_1D : same as above, but with implicit diffusion only along Z; for optimal parallel performance this option should be combined with PENCIL_AXIS=3
• PENCIL_AXIS : sets the default pencil direction, one of [1,2,3] for [X,Y,Z]-aligned pencils; X-aligned is the default and should be optimal for all cases except for Z implicit diffusion, where using Z-pencils is recommended
• SINGLE_PRECISION : calculation will be carried out in single precision (the default precision is double)
• GPU : enable GPU-accelerated runs
• USE_NVTX : enable NVTX tags for profiling

Input file

The input file input.nml sets the physical and computational parameters. In the examples/ folder are examples of input files for several canonical flows. See INFO_INPUT.md for a detailed description of the input file.

Files out1d.h90, out2d.h90 and out3d.h90 in src/ set which data are written in 1-, 2- and 3-dimensional output files, respectively. The code should be recompiled after editing out?d.h90 files.

Running the code

Run the executable with mpirun with a number of tasks complying to what has been set in the input file dns.in. Data will be written by default in a folder named data/, which must be located where the executable is run (by default in the run/ folder).

Visualizing field data

See INFO_VISU.md.

Contributing

We appreciate any contributions and feedback that can improve CaNS. If you wish to contribute to the tool, please get in touch with the maintainers or open an Issue in the repository / a thread in Discussions. Pull Requests are welcome, but please propose/discuss the changes in an linked Issue first.

Final notes

Please read the ACKNOWLEDGEMENTS, LICENSE files.