This movie shows two solutions of the advection equation on a sphere using triangular Lagrangian particles and panels. The passive scalar field being advected is a discontinuous block M.
The velocity field is deformational, but reversible, so that the solution at t=5 should be identical to the initial condition. This test case is designed to expose numerical errors in advection schemes : any differences between the final time and the initial time are due to numerical error.
The only difference between the two panels is the remeshing procedure. In the left panel, the new "Lagrangian remeshing" procedure is used, while the right hand panel shows the direct remeshing procedure typically used in Lagrangian simulations. The Lagrangian remeshing procedure is designe to preserve tracer ranges exactly and introduce no mixing due to numerical error.