A family of second order time stepping methods for the Darcy-Brinkman equations

Cibik A., DEMİR M., KAYA MERDAN S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.472, no.1, pp.148-175, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 472 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1016/j.jmaa.2018.11.015
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.148-175
  • Keywords: Darcy-Brinkman, Curvature stabilization, Double diffusion, DIFFUSIVE NATURAL-CONVECTION, OPPOSING TEMPERATURE, FINITE-ELEMENT, 2-LEVEL METHOD, SCHEMES, CAVITY
  • Middle East Technical University Affiliated: Yes

Abstract

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing the curvature for velocity, temperature and concentration equations. Accuracy in time is proven and the convergence results for the fully discrete solutions of problem variables are given. Several numerical examples including a convergence study are provided that support the derived theoretical results and demonstrate the efficiency and the accuracy of the method. (C) 2018 Elsevier Inc. All rights reserved.