Long time stability of a classical efficient scheme for an incompressible two-phase flow model

Article type: Research Article

Authors: Tachim Medjo, T.^{a; *} | Tone, F.^b

Affiliations: [a] Department of Mathematics and Statistics, Florida International University, Miami, FL, USA. E-mail: tachimt@fiu.edu | [b] Department Mathematics and Statistics, University of West Florida, Pensacola, FL, USA. E-mail: ftone@uwf.edu

Correspondence: [*] Corresponding author: T. Tachim Medjo, Department of Mathematics and Statistics, Florida International University, DM413B, University Park, Miami, FL 33199, USA. E-mail: tachimt@fiu.edu.

Abstract: In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

Keywords: semi-implicit scheme, long-time stability, incompressible two-phase flow, discrete attractors

DOI: 10.3233/ASY-151325

Journal: Asymptotic Analysis, vol. 95, no. 1-2, pp. 101-127, 2015