Continuous Data Assimilation for the Double-Diffusive Natural Convection

TL;DR

This paper develops and analyzes a continuous data assimilation algorithm for double-diffusive natural convection, demonstrating its stability, convergence, and effectiveness through numerical tests.

Contribution

It introduces a new data assimilation scheme with proven stability and convergence for a complex convection model, validated by numerical experiments.

Findings

The algorithm is stable over long times.

Convergence is proven for various nudging parameters.

Numerical tests confirm theoretical results.

Abstract

In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in space. The long time stability and convergence results are presented for different options of nudging parameters. Two elaborative numerical test are given in order to confirm the theory and prove the promise of the algorithm.