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 code is more flexible as it uses Gauss elimination. There the grid can also be non-uniform.
Update
CaNS now allows for choosing an implicit temporal discretization of the diffusion term of the N-S equations. This results in solving a Helmholtz equation for each of the velocity component. Since FFT-based solvers are also used, the same options described above for pressure BCs apply to the velocity boundary conditions.
Some features are:
- Hybrid MPI/OpenMP parallelization
- FFTW guru interface 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
- 2DECOMP&FFT routines used for performing global data transpositions and data i/o
- 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 developping channel
- periodic or developping square duct
- tri-periodic domain
- lid-driven cavity
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 expensive iterative solvers -- when fast 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 ficticious domain methods).
The fluid flow is solved with a second-order finite-volume 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 the price of higher computational demand, the diffusion term can be treated implicitly. (see e.g. Wesseling, Principles of computational fluid dynamics. Vol. 29. Springer Science & Business Media, 2009).
The input (header) files inside the src/ folder, setup.h90 and bc.h90 setup a case. setup.h90 sets most of the physical and computational parameters, and bc.h90 the boundary conditions for the Pressure and velocity fields, together with some options for forcing the flow and inflow/outflow conditions. The comments in these files make them self-explanatory.
In the examples/ folder are examples of these files for several canonical flows.
After modifying files setup.h90 and bc.h90 the code should be compiled.
The following prerequisites are needed:
- MPI
- FFTW3
- LAPACK
- BLAS
- OpenMP (optional)
The Makefile should be modified in agreement to the installation paths of each library. Also, the following preprocessor options are available:
-DDEBUG: performs some basic checks for debugging purposes-DTIMING: wall-clock time per timestep is computed-DIMPDIFF: diffusion term of the N-S equations is treated implicitly (thereby increasing the stability of the numerical algorithm for viscous-dominated flows)
Run the executable with mpirun with a number of tasks and shared threads complying to what has been set in the input file setup.h90. Data will be written by defailt in a folder named data, which must be located where the executable is run.
This is the first open-source release of this tool. I appreciate any feedback that can improve it. Also, you are encouraged to send case files pertaining to flows not listed in the examples folder. Comments/suggestions can be sent to p.simoes.costa@gmail.com.
Please read the ACKNOWLEDGEMENTS and LICENSE files.
Pedro Costa (p.simoes.costa@gmail.com)