In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.
Y. Gao et al., "Second-Order, Fully Decoupled, Linearized, and Unconditionally Stable Scalar Auxiliary Variable Schemes for Cahn–Hilliard–Darcy System," Numerical Methods for Partial Differential Equations, vol. 38, no. 6, pp. 1658 - 1683, Wiley, Nov 2022.
The definitive version is available at https://doi.org/10.1002/num.22829
Mathematics and Statistics
Keywords and Phrases
Cahn–Hilliard–Darcy system; finite element method; fully decoupled; scalar auxiliary variable approach; second-order; unconditional stability
International Standard Serial Number (ISSN)
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01 Nov 2022