Flux-corrected summation-by-parts finite-difference solver for atmospheric transport

Summation-by-Parts Finite-Difference (SBP-FD) methods are widely used to construct stable, high-order accurate spatial discretizations for hydrodynamics and continuum mechanics. This article presents a locally mass-conserving and monotonic SBP-FD scheme for a tracer advection equation in the flux form. Our approach reformulates the SBP-FD spatial discretization in a finite-volume manner, expressing it as the difference of fluxes across grid cell interfaces. These fluxes are limited using the Flux-Corrected Transport (FCT) method. The resulting scheme preserves monotonicity in terms of the tracer specific concentration – the ratio of tracer density to dry air density. Achieving this required modifications to the standard FCT limiter operating on tracer density. The proposed numerical scheme is evaluated using a standard suite of test cases relevant to atmospheric modelling, demonstrating accuracy comparable to state-of-the-art methods. For smooth tracer distributions, the scheme demonstrates second-order accuracy in the ℓ 2 -norm. Strict monotonicity is verified for discontinuous initial conditions and wind fields that severely deform the tracer into thin filaments, including divergent wind fields.