rustpde

rustpde: Spectral method solver for Navier-Stokes equations

Dependencies

• cargo >= v1.49
• hdf5 (sudo apt-get install -y libhdf5-dev)

Important

OpenBlas's multithreading conflicts with internal multithreading. Turn it off for better performance:

export OPENBLAS_NUM_THREADS=1

Details

This library is intended for simulation softwares which solve the partial differential equations using spectral methods.

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

• Chebyshev (Orthonormal), see [chebyshev()]
• ChebDirichlet (Composite), see [cheb_dirichlet()]
• ChebNeumann (Composite), see [cheb_neumann()]
• FourierR2c (Orthonormal), see [fourier_r2c()]

Composite basis combine several basis functions of its parent space to satisfy the needed boundary conditions, this is often called a Galerkin method.

Implemented solver

• 2-D Rayleigh Benard Convection: Direct numerical simulation, see [navier::navier]
• 2-D Rayleigh Benard Convection: Steady state solver, see [navier::navier_adjoint]

Example

Solve 2-D Rayleigh Benard Convection ( Run with cargo run --release )

use rustpde::integrate;
use rustpde::navier::Navier2D;
use rustpde::Integrate;

fn main() {
    // Parameters
    let (nx, ny) = (64, 64);
    let ra = 1e5;
    let pr = 1.;
    let adiabatic = true;
    let aspect = 1.0;
    let dt = 0.02;
    let mut navier = Navier2D::new(nx, ny, ra, pr, dt, aspect, adiabatic);
    // Set initial conditions
    navier.set_velocity(0.2, 1., 1.);
    // // Want to restart?
    // navier.read("data/flow100.000.h5");
    // Write first field
    navier.callback();
    integrate(&mut navier, 100., Some(1.0));
}

Solve 2-D Rayleigh Benard Convection with periodic sidewall

use rustpde::integrate;
use rustpde::navier::Navier2D;
use rustpde::Integrate;

fn main() {
    // Parameters
    let (nx, ny) = (64, 64);
    let ra = 1e5;
    let pr = 1.;
    let aspect = 1.0;
    let dt = 0.02;
    let mut navier = Navier2D::new_periodic(nx, ny, ra, pr, dt, aspect);
    integrate(&mut navier, 100., Some(1.0));
}

Postprocess the output

rustpde contains a python folder with some scripts. 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 python/plot2d.py

or create an animation

python3 python/anim2d.py

Paraview

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

./bin/create_xmf.

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

Documentation

Download and run:

cargo doc --open