PyMPDATA_examples

Introduction

PyMPDATA examples are bundled with PyMPDATA and located in the examples subfolder. They constitute a separate PyMPDATA_examples Python package which is also available at PyPI. The examples have additional dependencies listed in PyMPDATA_examples package setup.py file. Running the examples requires the PyMPDATA_examples package to be installed.

We recommend you look through the example gallery below to see the examples in action.

Example gallery

Unless stated otherwise the following examples solve the basic advection equation: $$ \partial_t (\psi) + \nabla \cdot (u \psi) = 0 $$

The examples are grouped by the dimensionality of the computational grid.

in 1D

tags	link
advection-diffusion equation $$ \partial_t (\psi) + \nabla \cdot (u \psi) + \mu \Delta (\psi) = 0 $$	`PyMPDATA_examples.advection_diffusion_1d`*
Black-Scholes equation, option pricing $$ \frac{\partial f}{\partial t} + rS \frac{\partial f}{\partial S} + \frac{\sigma^2}{2} S^2 \frac{\partial^2 f}{\partial S^2} - rf = 0$$	`PyMPDATA_examples.Arabas_and_Farhat_2020`*
advection equation, homogeneous, several algorithm variants comparison: infinite-gauge, flux-corrected,..	`PyMPDATA_examples.Smolarkiewicz_2006_Figs_3_4_10_11_12`
Size-spectral advection, particle population condensational growth, coordinate transformation $$ \partial_t (G \psi) + \nabla \cdot (Gu \psi) = 0 $$	`PyMPDATA_examples.Olesik_et_al_2022`*
advection equation, double-pass donor-cell option	`PyMPDATA_examples.DPDC`

in 2D

tags	link
advection-diffusion equation $$ \partial_t (\psi) + \nabla \cdot (u \psi) + \mu \Delta (\psi) = 0 $$	`PyMPDATA_examples.advection_diffusion_2d`*
Spectral-spatial advection, particle population condensational growth in a vertical column of air, time dependent flow	`PyMPDATA_examples.Shipway_and_Hill_2012`
shallow-water equations $$\begin{eqnarray} \partial_t h + \partial_x (uh) + \partial_y (vh) &=& 0~ \\ \partial_t (uh) + \partial_x ( uuh) + \partial_y (vuh) &=& - h \partial_x h~ \\ \partial_t (vh) + \partial_x ( uvh) + \partial_y (vvh) &=& - h \partial_y h~ \end{eqnarray}$$	`PyMPDATA_examples.Jarecka_et_al_2015`*
advection equation, solid body rotation	`PyMPDATA_examples.Molenkamp_test_as_in_Jaruga_et_al_2015_Fig_12`*
advection equation, coordinate transformation, spherical coordinates, see also examples in PyMPDATA-MPI $$ \partial_t (G \psi) + \nabla \cdot (Gu \psi) = 0 $$	`PyMPDATA_examples.Williamson_and_Rasch_1989_as_in_Jaruga_et_al_2015_Fig_14`
advection equation, comparison against DG solution using Trixi.jl	`PyMPDATA_examples.trixi_comparison`

in 3D

tags	link
homogeneous advection equation	`PyMPDATA_examples.Smolarkiewicz_1984`
homogeneous advection equation, performance comparison against libmpdata++, scalability analysis in respect to threads	`PyMPDATA_examples.Bartman_et_al_2022`

* - with comparison against analytic solution

Installation

Since the examples package includes Jupyter notebooks (and their execution requires write access), the suggested install and launch steps are:

git clone https://github.com/open-atmos/PyMPDATA-examples.git
cd PyMPDATA-examples
pip install -e .
jupyter-notebook

Alternatively, one can also install the examples package from pypi.org by using

pip install PyMPDATA-examples.

View Source

 1"""
 2.. include:: ../docs/pympdata_examples_landing.md
 3"""
 4
 5from importlib.metadata import PackageNotFoundError, version
 6
 7try:
 8    __version__ = version(__name__)
 9except PackageNotFoundError:
10    # package is not installed
11    pass