On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case
Abstract
We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 19, 2020
- Source ID
- 10.1142/s0218202520500438
Entities
People
- Jie Shen
- Xiaoli Li
Organizations
- Air Force Office of Scientific Research
- China Postdoctoral Science Foundation
- National Natural Science Foundation of China
- National Science Foundation
- Purdue University
- Xiamen University