Modeling advection in geophysical flows with particle level sets

We have applied, for the first time in geodynamical flows, the Particle Level Set method for advecting compositional fields with sharp discontinuities. This robust and efficient Eulerian‐Lagrangian technique is based on the concept of Implicit Surfaces, which allows the use of high order accurate numerical schemes in the vicinity of discontinuities. We have tested the Particle Level Set method against the robust and popular Tracer‐in‐Cell method on well‐known 2D thermochemical benchmarks and typical 3D convective flows. The use of Lagrangian tracers in the Particle Level Set method yields accurate solutions of purely advective transport, where sub‐grid scale features can be resolved. In every case we ran we found that the Particle Level Set method accuracy equals or is better than the popular Tracer‐in‐Cell method, and can lead to significantly smaller computational cost, in particular in three‐dimensional flows, where the reduction of computational time for modeling advection processes is most needed.