Parameter Analysis in Continuous Data Assimilation for Various Turbulence Models

TL;DR

This paper analyzes how parameter estimation affects data assimilation in turbulence models, using numerical simulations to validate theoretical insights for the Bardina and Navier-Stokes-α models.

Contribution

It provides a detailed parameter estimation analysis for turbulence models within a data assimilation framework, supported by numerical validation.

Findings

Parameter estimation improves model accuracy

Numerical results confirm theoretical predictions

Interpolant operators effectively incorporate observational data

Abstract

In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier-Stokes-{\alpha} model. Our approach involves creating an approximate solution for the turbulence models by employing an interpolant operator based on the observational data of the systems. The estimation depends on the parameter alpha in the models. Additionally, numerical simulations are presented to validate our theoretical results