An unconditional energy stable data assimilation scheme for Navier-Stokes-Cahn-Hilliard equations with local discretized observed data

Xin Song, Qing Xia, Junseok Kim, Yibao Li

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce the modified Navier-Stokes-Cahn-Hilliard equations with a data assimilation term to utilize the information of the observed data. Based on the idea of feedback control, this term nudges the solutions to the observed data sampled from the reference process. By utilizing the Crank-Nicolson formula and the scalar auxiliary variable approach, we introduce an efficient numerical scheme for the modified Navier-Stokes-Cahn-Hilliard equations. Properties of the mass conservation and unconditional energy stability are proved. We explore the robustness and efficiency of the proposed scheme with various experiments.

Original languageEnglish
Pages (from-to)21-33
Number of pages13
JournalComputers and Mathematics with Applications
Volume164
DOIs
Publication statusPublished - 2024 Jun 15

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd

Keywords

  • Date assimilation
  • Navier-Stokes-Cahn-Hilliard equations
  • Second-order accuracy
  • Unconditionally stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Fingerprint

Dive into the research topics of 'An unconditional energy stable data assimilation scheme for Navier-Stokes-Cahn-Hilliard equations with local discretized observed data'. Together they form a unique fingerprint.

Cite this