Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System

Abstract

In this article we propose the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system that models thermal convection of two-phase flows in a fluid layer overlying a porous medium. Based on operator splitting and pressure stabilization we propose a family of fully decoupled numerical schemes such that the Navier-Stokes equations, the Darcy equations, the heat equation and the Cahn-Hilliard equation are solved independently at each time step, thus significantly reducing the computational cost. We show that the schemes preserve the underlying energy law and hence are unconditionally long-time stable. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

National Science Foundation, Grant DMS-1912715

Keywords and Phrases

Convection; Phase field model; Two-phase flow; Unconditional stability

International Standard Serial Number (ISSN)

0885-7474; 1573-7691

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Springer, All rights reserved.

Publication Date

01 Nov 2020

Link to Full Text

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