PyMPDATA is a high-performance Numba-accelerated Pythonic implementation of the MPDATA algorithm of Smolarkiewicz et al. for numerically solving generalised transport equations - partial differential equations used to model conservation/balance laws, scalar-transport problems, convection-diffusion phenomena (in geophysical fluid dynamics and beyond). As of the current version, PyMPDATA supports homogeneous transport in 1D, 2D and 3D (work in progress) using structured meshes, optionally generalised by employment of a Jacobian of coordinate transformation. PyMPDATA includes implementation of a set of MPDATA variants including the non-oscillatory option, infinite-gauge, divergent-flow, double-pass donor cell (DPDC) and third-order-terms options. It also features support for integration of Fickian-terms in advection-diffusion problems using the pseudo-transport velocity approach. In 2D and 3D simulations, domain-decomposition is used for multi-threaded parallelism.


PyMPDATA is engineered purely in Python targeting both performance and usability, the latter encompassing research users', developers' and maintainers' perspectives. From researcher's perspective, PyMPDATA offers hassle-free installation on multitude of platforms including Linux, OSX and Windows, and eliminates compilation stage from the perspective of the user. From developers' and maintainers' perspective, PyMPDATA offers a suite of unit tests, multi-platform continuous integration setup, seamless integration with Python development aids including debuggers and profilers.

PyMPDATA design features a custom-built multi-dimensional Arakawa-C grid layer allowing to concisely represent multi-dimensional stencil operations. The grid layer is built on top of NumPy's ndarrays (using "C" ordering) using Numba's @njit functionality for high-performance array traversals. It enables one to code once for multiple dimensions, and automatically handles (and hides from the user) any halo-filling logic related with boundary conditions.

PyMPDATA ships with a set of examples/demos offered as github-hosted Jupyer notebooks offering single-click deployment in the cloud using or using The examples/demos reproduce results from several published works on MPDATA and its applications, and provide a validation of the implementation and its performance.