Lagrangian advection scheme with shape matrix (LASM) v0.2: Interparcel mixing, physics-dynamics coupling and 3-D extension

The interparcel mixing algorithm in the Lagrangian advection scheme with shape matrix (LASM) is updated to make the scheme more robust. The linear degeneration criterion is replaced by the maximum deviation of the skeleton points so that the new algorithm is more effective in controlling the shape of parcels, which is vital for long time simulation. LASM is inherently shape-preserving without any complicated filter or limiter, and it is linear. This fact contributes to the ability to preserve the sum of multiple tracers exactly on the parcels in LASM. A newly proposed terminator "toy"-chemistry test is used to test LASM, which shows that LASM can preserve the weighted sum of two reactive species precisely. The physics-dynamics coupling (i.e., tendency evaluation type) is also discussed. A flow generated by a WRF large-eddy simulation is also used to test the 3-D extension of LASM.