Open source software developed in the team :

• samurai

https://github.com/hpc-maths/samurai

The use of mesh adaptation methods in numerical simulation can significantly reduce the memory footprint and computational costs. Different types of methods exist: patch-based AMR, cell-based AMR, cell-based or point-based multiresolution, etc.

Various open-source software packages are available to the community to manage mesh adaptation: AMReX for patch-based AMR, p4est and pablo for cell-based adaptation.

The strength of samurai is that it enables all the above mesh adaptation methods to be implemented from the same data structure. The mesh is represented in the form of intervals, and a set algebra is used to efficiently search for subsets within these intervals. Samurai also offers a flexible, user-friendly interface for easy implementation of numerical methods.

• ponio

https://github.com/hpc-maths/ponio

The aim of ponio is to provide a set of schemes in time for solving a whole collection of ODEs and PDEs. It is initially written in C++, but various interfaces will later be available for use in other languages widely used in the scientific community (Python and Julia, for example). The aim here is to discuss the various strategies for the temporal integration of PDEs. The simplest is the combination of an operator separation strategy and a line method involving various classical time integrators (RADAU5, ROCK4, IMEX... ); the long-term objective is also to be able to tackle innovative adaptive code coupling techniques through an interface (Conjugate heat transfer, surface combustion...) as well as classes of time-space coupled schemes (Lax-Wendroff, OSMP, time-space coupled IMEX with good asymptotic preserving and stability properties...).

• josiepy

https://github.com/hpc-maths/josiepy

The aim here is to provide a Python tool capable of solving 1D and 2D finite volume (or even Discontinuous Galerkin) problems on potentially deformed Cartesian meshes in an efficient way, with a view to rapid prototyping. The code is versatile but has been used extensively in the simulation of two-phase flows with interface dynamics and methods of moments.

• pylbm

https://github.com/pylbm/pylbm

pylbm is an all-in-one package for numerical simulations using Boltzmann lattice methods. This package provides all the tools to describe a Boltzmann lattice scheme for 1D, 2D, and 3D problems. The D'Humières formalism has been chosen to describe the problem. It is possible to read complex geometries and perform calculations on them.

pylbm lets you formally define the lattice Boltzmann scheme you wish to use, enabling you to perform stability analyses and give equivalent equations (physical equations solved). Indeed, one of the major problems with these methods is that we start from the scheme and work our way back to the physical equations we wish to solve. In the usual methods (finite differences, finite volumes, finite elements, etc.), we start from the equations that we discretize to arrive at our numerical scheme. This change of point of view can be very restrictive for the unaccustomed user. pylbm therefore offers a set of tools for a better understanding of these methods.

Finally, starting from formal writing, pylbm is able to generate the numerical code associated with the schemes described for different target architectures: CPU, GPU with shared or distributed memory. This code generation is easily extensible.