On the implementation of flux limiters in algebraic frameworks
Abstract
The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are of paramount importance for the temporal integration of highspeed aerodynamics, multiphase flows and hyperbolic equations in general.
Meanwhile, the breakthrough of new computing architectures and the hybridization of supercomputer systems pose a huge portability challenge, particularly for legacy codes, since the computing subroutines that form the algorithms, the socalled kernels, must be adapted to various complex parallel programming paradigms. From this perspective, the development of innovative implementations relying on a minimalist set of kernels simplifies the deployment of scientific computing software on stateoftheart supercomputers, while it requires the reformulation of algorithms, such as the aforementioned flux limiters.
Equipped with basic algebraic topology and graph theory underlying the classical mesh concept, a new flux limiter formulation is presented based on the adoption of algebraic data structures and kernels. As a result, traditional flux limiters are cast into a stream of only two types of computing kernels: sparse matrixvector multiplication and generalized pointwise binary operators. The newly proposed formulation eases the deployment of such a numerical technique in massively parallel, potentially hybrid, computing systems and is demonstrated for a canonical advection problem.
 Publication:

Computer Physics Communications
 Pub Date:
 February 2022
 DOI:
 10.1016/j.cpc.2021.108230
 arXiv:
 arXiv:2110.03044
 Bibcode:
 2022CoPhC.27108230V
 Keywords:

 Flux limiter;
 Parallel CFD;
 Heterogeneous computing;
 Portability;
 Mimetic;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 doi:10.1016/j.cpc.2021.108230