Abstract
The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free,
WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational
properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in
efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates
a range of choices for the user when approaching their specific application while maintaining good
parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping,
strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronization and
data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves
upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is
evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively
and qualitatively what a user should expect when employing this method in their application.
