Communications in Mathematical Sciences
Volume 18 (2020)
Numerical study of compressible Navier–Stokes–Cahn–Hilliard system
Pages: 571 – 591
In this paper, we present a relaxation scheme coupled with a stabilized method to numerically study the compressible Navier–Stokes–Cahn–Hilliard system, which has energy-decaying property under certain conditions. Numerical simulations are carried out to verify the stability of the scheme. Numerical results show that the average concentration difference for the two components of the initial state determines the long-time behavior of the diffusive interface for the two-phase flow, which are consistent with theoretical asymptotic stability results established by the authors.
relaxation scheme, Navier–Stokes, Cahn–Hilliard, phase transition, large-time behavior
2010 Mathematics Subject Classification
35L65, 65D30, 65M06, 76T10
The authors’ research was supported in part by National Key R & D Program of China (2018YFC0830300) and NSFC (No. 11201322, No. 11671027, No. 11971020).
Received 3 January 2019
Accepted 8 November 2019
Published 20 June 2022