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• W4378839596 endingPage "115363" @default.
• W4378839596 startingPage "115363" @default.
• W4378839596 abstract "A fully decoupled, linearized, and unconditionally stable finite element method is developed to solve the Cahn-Hilliard-Navier–Stokes-Darcy model in the coupled free fluid region and porous medium region. By introducing two auxiliary energy variables, we derive the equivalent system that is consistent with the original system. The energy dissipation law of the proposed equivalent model is proven. To lay a solid foundation, we first present a coupled linearized time-stepping method for the reformulated system, and prove its unconditionally energy stability. In order to further improve the computational efficiency, special treatment for the interface conditions and the artificial compression approach are utilized to decouple the two subdomains and the Navier–Stokes equation. Therefore, with the discretization techniques of two existing auxiliary variable approaches, a fully decoupled and linearized numerical scheme can be developed, under the framework of a semi-implicit semi-explicit scheme for temporal discretizaion and Galerkin finite element method for spatial discretization. The grad-div stabilization is also employed to further improve the stability of auxiliary variable algorithm. The full discretization obeys the desired energy dissipation law without any temporal restriction. Moreover, the implementation process is discussed, including the adaptive mesh strategy to accurately capture the diffuse interface. Ample numerical experiments are performed to validate the typical features of developed numerical schemes, such as the accuracy, energy stability without restriction for time step size, and adaptive mesh refinement in space. Furthermore, we apply the proposed numerical method to simulate the shape relaxation and the Buoyancy-driven flows, which demonstrate the applicability of the proposed method." @default.
• W4378839596 created "2023-06-01" @default.
• W4378839596 creator A5026611351 @default.
• W4378839596 creator A5041708794 @default.
• W4378839596 creator A5081675173 @default.
• W4378839596 creator A5088723986 @default.
• W4378839596 date "2024-01-01" @default.
• W4378839596 modified "2023-09-29" @default.
• W4378839596 title "A fully decoupled numerical method for Cahn–Hilliard–Navier–Stokes–Darcy equations based on auxiliary variable approaches" @default.
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