Ensemble Kalman Filter for Non-Conservative Adaptive Meshes and Lagrangian Observations With a Joint Physics and Mesh Update.

Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing important or unresolved physics. The adaptation can be informed by the model state, external information, or made to depend on the model physics. In the case of a Lagrangian solver the mesh is driven by the flow and one may think of the mesh configuration as a part of the model state. If observational data is to be assimilated into the model, the question of updating the mesh configuration with the physical values arises. In previous work we developed a novel strategy to assimilate Eulerian observations updating the mesh configuration as well as the physical values of the model. We now study the case where the observations are Lagrangian and driven by the same flow that drives the adaptive mesh. We find significant advantages to including the mesh configuration to be a part of the model state over not doing so in the presence of these observations. We also find advantages beyond traditional metrics such as RMSE.