English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work, we combine a stochastic model reduction with a particle filteraugmented with tempering and jittering, and apply the combined algorithm to adamped and forced incompressible 2D Euler dynamics defined on a simplyconnected bounded domain.  We show that using the combined algorithm, we are able to assimilate datafrom a reference system state (the ``truth") modelled by a highly resolvednumerical solution of the flow that has roughly $3.1\times10^6$ degrees offreedom, into a stochastic system having two orders of magnitude less degreesof freedom, which is able to approximate the true state reasonably accuratelyfor $5$ large scale eddy turnover times, using modest computational hardware.  The model reduction is performed through the introduction of a stochasticadvection by Lie transport (SALT) model as the signal on a coarser resolution.The SALT approach was introduced as a general theory using a geometricmechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows onthe numerical implementation for SALT presented by Cotter et al, SIAMMultiscale Model. Sim. (2019) for the flow in consideration. The modelreduction is substantial: The reduced SALT model has $4.9\times 10^4$ degreesof freedom.  Results from reliability tests on the assimilated system are also presented.

A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation