  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 high-speed 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 so-called 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 state-of-the-art 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 matrix-vector 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.
