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In this paper, we design a decoupled, linear, unconditionally stable and fully discrete numerical scheme for a ferrohydrodynamics system with second‐order temporal accuracy. This scheme is based on a second‐order backward difference formula for time derivative terms and linearization extrapolation for nonlinear terms, which produces a series of decoupled linear equations and solves effectively this nonlinear and multiphysical coupled system. Meanwhile, we show that the scheme is unconditionally stable. Finally, some numerical experiments are provided to verify the theoretical finding and illustrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

The standard eddy viscosity model is commonly used to simulate turbulence, but there exist difficulties in simulating the backscatter of the non-statistical equilibrium turbulence. In this work, we construct a novel modified eddy viscosity model based on a simplified Cebeci–Smith equation, which is applied to the non-equilibrium turbulence. Moreover, we analyze some properties of the model and propose a fully discrete scheme, which is proven to be stable and convergent. Finally, some numerical examples are presented to test the theoretical prediction of the proposed scheme, and intermittent backscatter is captured and observed by simulating the established model. [ABSTRACT FROM AUTHOR]

In this paper, we design a decoupled scheme for solving a fluid–fluid interaction problem, which includes two Navier–Stokes equations coupled by some nonlinear interface conditions. Compared with two decoupled schemes proposed by Connors et al. (2012, Decoupled time stepping methods for fluid–fluid interaction. SIAM J. Numer. Anal. , 50 , 1297–1319) for the fluid–fluid interaction problem, we deal with these nonlinear interface conditions by applying explicit scheme. The presented fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the first-order backward Euler scheme for temporal discretization and explicit treatment for the interface conditions and the nonlinear terms. Moreover, the unconditional energy stability is established and error estimate for the fully discrete scheme is also showed. Finally, some numerical experiments are provided to verify the theoretical results, which illustrate the accuracy and efficiency of the presented scheme. [ABSTRACT FROM AUTHOR]

Several iterative finite element methods are analyzed for a steady‐state double‐diffusive natural convection model, which contains the diffusion of temperature and concentration and can simulate heat and mass transfer phenomena. These iterations include the Stokes‐type, Newton‐type, and Oseen‐type iterative methods. Then, based on the uniqueness condition, stability and convergence of these iterative methods are proved for the considered model. Finally, some numerical examples are presented for validating the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we study a multi-physics model for the closed-loop geothermal system consisting of some pipelines and a reservoir. The mathematical model for simulating this system mainly focuses on heat transfer between porous media in the reservoir and fluid flow in the pipelines. Besides, to describe the fluid and heat transfer in two regions, the governing equations of the mathematical model are denoted by the steady Navier-Stokes/Darcy equations coupled with the convection-diffusion equations. Next, we design a perturbation system to prove the well-posedness of the governing equations. Moreover, in variational formulation, a Nitsche's penalty term is added to overcome the difficulty of instability caused by the interface condition of heat flux. Furthermore, a decoupled iterative algorithm is proposed to solve the considered equations based on the finite element method, and the stability and convergence of the presented algorithm are shown. Finally, some numerical tests are performed to verify the accuracy and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we first established a high-accuracy difference scheme for the time-fractional Schrödinger equation (TFSE), where the factional term is described in the Caputo derivative. We used the L1-2-3 formula to approximate the Caputo derivative, and the fourth-order compact finite difference scheme is utilized for discretizing the spatial term. The unconditional stability and convergence of the scheme in the maximum norm are proved. Finally, we verified the theoretical result with a numerical test. [ABSTRACT FROM AUTHOR]

This paper presents a grad‐div stabilization with the Jacobi iteration to the thermally coupled incompressible magnetohydrodynamic system, which avoids breakdown of solver and increase of computational time with increasing value of grad‐div stabilized parameter. The proposed method includes two steps: a fully discrete first‐order Euler semi‐implicit scheme based on the mixed finite element method is implemented for the considered problem in Step 1. Then, in Step 2, the Jacobi approximation is applied to the grad‐div operator whose each component will be decoupled. Moreover, we obtain theoretical analysis results of the presented method, both unconditional stability and convergence analysis. Finally, some numerical experiments are presented to show the accuracy and verify effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]