Adaptively implicit advection for atmospheric flows

This adaptively implicit advection scheme facilitates efficient and robust integrations with long time‐steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes.

A novel and important aspect for the efficiency of the approach is that only one iteration is needed each time the linear equation solver is called for solving the advection equation. The demonstration in this paper uses the second‐order Runge‐Kutta implicit/explicit time integration in combination with a second/third‐order finite‐volume spatial discretization and is tested using deformation flow tracer advection on the sphere and a fully compressible model for atmospheric flows.