libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

TL;DR

libmpdata++ 0.1 is an open-source C++ library providing parallel, stable, and versatile solvers for systems of generalised transport equations using the MPDATA algorithm, with extensive examples and benchmarks.

Contribution

This paper introduces libmpdata++, a comprehensive C++ library implementing advanced MPDATA solvers with parallelisation and multiple accuracy options for transport equations.

Findings

Library supports second and third-order MPDATA formulations

Includes flux-corrected transport for non-oscillatory solutions

Demonstrated on diverse transport and fluid dynamics problems

Abstract

This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensioanl array containers, and is released as free/libre and open-source software.