DeepAI AI Chat
Log In Sign Up

Ensemble Kalman Filter for non-conservative moving mesh solvers with a joint physics and mesh location update

by   Christian Sampson, et al.

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 this latter case, one can think of the mesh configuration as 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. Adaptive meshes present significant challenges when using popular ensemble Data Assimilation (DA) methods. We develop a novel strategy for ensemble-based DA for which the adaptive mesh is updated along with the physical values. This involves including the node locations as a part of the model state itself allowing them to be updated automatically at the analysis step. This poses a number of challenges which we resolve to produce an effective approach that promises to apply with some generality. We evaluate our strategy with two testbed models in 1-d comparing to a strategy that does not update the mesh configuration. We find updating the mesh improves the fidelity and convergence of the filter.


page 15

page 16

page 17

page 18

page 21

page 22

page 23

page 24


A Metric Tensor Approach to Data Assimilation with Adaptive Moving Meshes

Adaptive moving spatial meshes are useful for solving physical models gi...

Ensemble updating of binary state vectors by maximising the expected number of unchanged components

In recent years, several ensemble-based filtering methods have been prop...

An hr-Adaptive Method for the Cubic Nonlinear Schrödinger Equation

The nonlinear Schrödinger equation (NLSE) is one of the most important e...

Analysis of a localised nonlinear Ensemble Kalman Bucy Filter with complete and accurate observations

Concurrent observation technologies have made high-precision real-time d...

Anisotropic mesh adaptation in Firedrake with PETSc DMPlex

Despite decades of research in this area, mesh adaptation capabilities a...

A generalised and fully Bayesian framework for ensemble updating

We propose a generalised framework for the updating of a prior ensemble ...

Anisotropic Mesh Filtering by Homogeneous MLS Fitting

In this paper we present a novel geometric filter, a homogeneous moving ...