rustpde

rustpde: Spectral method solver for Navier-Stokes equations

Dependencies

• cargo >= v1.49
• hdf5 (sudo apt-get install -y libhdf5-dev)
• clang (only for parallel simulations, see MPI.)

This version of rustpde contains serial and mpi-parallel examples of fluid simulations using the spectral method.

MPI

The mpi crate relies on a installed version of libclang. Also make sure to add the clang bin folder to the path variable, i.e. for example

• export PATH="${INSTALL_DIR}/llvm-project/build/bin:$PATH"

The correct mpi installation can be tricky at times. If you want to use this library without mpi, you can disable of the default mpi feature. Note that, if default features are turned off, do not forget to specify which openblas backend you want to use. For example:

• cargo build --release --no-default-features --features openblas-static

OpenBlas

By default rustpde uses ndarray's openblas-static backend, which is costly for compilation. To use a systems OpenBlas installation, disable default features, and use the openblas-system feature. Make sure to not forget to explicity use the mpi feature in this case, .i.e.

• cargo build --release --no-default-features --features mpi

Make sure the OpenBlas library is linked correctly in the library path, i.e.

• export LIBRARY_PATH="${INSTALL_DIR}/OpenBLAS/lib"

IT IS NOT LD_LIBRARY_PATH!

Openblas multithreading conflicts with internal multithreading. Turn it off for better performance:

• export OPENBLAS_NUM_THREADS=1

Hdf5

Install Hdf5 and link as follows:

• export HDF5_DIR="${INSTALL_DIR}/hdf5-xx/"
• export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:${HDF5_DIR}/lib"

Details

Currently rustpde implements transforms from physical to spectral space for the following basis functions:

• Chebyshev (Orthonormal), see [bases::chebyshev()]
• ChebDirichlet (Composite), see [bases::cheb_dirichlet()]
• ChebNeumann (Composite), see [bases::cheb_neumann()]
• ChebDirichletNeumann (Composite), see [bases::cheb_dirichlet_neumann()]
• FourierR2c (Orthonormal), see [bases::fourier_r2c()]
• FourierC2c (Orthonormal), see [bases::fourier_c2c()]

Composite basis combine several basis functions of its parent space to satisfy the boundary conditions, i.e. Galerkin method.

Implemented solver

• 2-D Rayleigh Benard Convection: Direct numerical simulation, see [navier_stokes::Navier2D] or [navier_stokes_mpi::Navier2DMpi]

Example

Solve 2-D Rayleigh Benard Convection ( Run with cargo mpirun --np 2 --bin rustpde )

use rustpde::mpi::initialize;
use rustpde::mpi::integrate;
use rustpde::navier_stokes_mpi::Navier2DMpi;

fn main() {
    // mpi
    let universe = initialize().unwrap();
    // Parameters
    let (nx, ny) = (129, 129);
    let (ra, pr, aspect) = (1e7, 1., 1.);
    let dt = 0.01;
    let mut navier = Navier2DMpi::new_confined(&universe, nx, ny, ra, pr, dt, aspect, "rbc");
    navier.write_intervall = Some(1.0);
    integrate(&mut navier, 10., Some(0.1));
}

Solve 2-D Rayleigh Benard Convection with periodic sidewall

use rustpde::mpi::initialize;
use rustpde::mpi::integrate;
use rustpde::navier_stokes_mpi::Navier2DMpi;

fn main() {
    // mpi
    let universe = initialize().unwrap();
    // Parameters
    let (nx, ny) = (128, 65);
    let (ra, pr, aspect) = (1e6, 1., 1.);
    let dt = 2e-3;
    let mut navier = Navier2DMpi::new_periodic(&universe, nx, ny, ra, pr, dt, aspect, "rbc");
    navier.write_intervall = Some(1.0);
    integrate(&mut navier, 10., Some(0.1));
}

Postprocess the output

rustpde contains some python scripts for postprocessing. If you have run the above example and specified to save snapshots, you will see hdf5 files in the data folder.

Plot a single snapshot via

python3 plot/plot2d.py

Paraview

The xmf files, corresponding to the h5 files can be created by the script

./tools/create_xmf.

This script works only for fields from the Navier2D solver with the attributes temp, ux, uy and pres. The tools folder contains also the full crate create_xmf, which can be adapted for specific usecases.

Documentation

Download and run:

cargo doc --open