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Purpose: The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton's iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally. Design/methodology/approach: Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes' iterative schemes are also analyzed under some strong uniqueness conditions. Findings: This work was supported by the NSF of China (No. 11971152). Originality/value: This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to further develop stator permanent magnet (PM) type memory machines by providing generalized design guidelines for double-stator memory machines (DSMMs) with hybrid PMs. This paper discusses the design experience of DSMMs and presents a comparative study of radial magnetization (RM) and circumferential magnetization (CM) types. Design/methodology/approach: It begins with an introduction to RM and CM operating principles and magnetization mechanisms. Then, a comparative study is conducted for one of the RM-DSMM rotor pole pairs, inner and outer stator clamping angles and low coercive force PMs thickness. Finally, the two machines' finite element simulation performance is compared. The validity of the proposed machine structure is demonstrated. Findings: In this paper, the double-stator structure is extended to parallel hybrid PM memory machines, and two novel DSMMs with RM and CM configurations are proposed. Two types of DSMMs have PMs and magnetizing windings on the inner stator and armature windings on the outer stator. The main difference between the two is the arrangement of PMs on the inner stator. Originality/value: Conventional stator PM memory machines have geometrical space conflicts between the PM and armature windings. The proposed double-stator structure can alleviate these conflicts and increase the torque density accordingly. In addition, this paper contributes to comparing the arrangement of hybrid PMs for DSMMs. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to design a simple and accurate a-posteriori Lagrangian-based error estimator is developed for the class of backward differentiation formula (BDF) algorithms with variable time step size, and the adaptive time-stepping in BDF algorithms is demonstrated for efficient time-dependent simulations in fluid flow and heat transfer. Design/methodology/approach: The Lagrange interpolation polynomial is used to predict the time derivative, and then the accurate primary result is obtained by the Gauss integral, which is applied to evaluate the local error. Not only the generalized formula of the proposed error estimator is presented but also the specific expression for the widely applied BDF1/2/3 is illustrated. Two essential executable MATLAB functions to implement the proposed error estimator are appended for practical applications. Then, the adaptive time-stepping is demonstrated based on the newly proposed error estimator for BDF algorithms. Findings: The validation tests show that the newly proposed error estimator is accurate such that the effectivity index is always close to unity for both linear and nonlinear problems, and it avoids under/overestimation of the exact local error. The applications for fluid dynamics and coupled fluid flow and heat transfer problems depict the advantage of adaptive time-stepping based on the proposed error estimator for time-dependent simulations. Originality/value: In contrast to existing error estimators for BDF algorithms, the present work is more accurate for the local error estimation, and it can be readily extended to practical applications in engineering with a few changes to existing codes, contributing to efficient time-dependent simulations in fluid flow and heat transfer. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to describe a novel universal error estimator and the adaptive time-stepping process in the generalized single-step single-solve (GS4-1) computational framework, applied for the fluid dynamics with illustrations to incompressible Navier–Stokes equations. Design/methodology/approach: The proposed error estimator is universal and versatile that it works for the entire subsets of the GS4-1 framework, encompassing the nondissipative Crank–Nicolson method, the most dissipative backward differential formula and anything in between. It is new and novel that the cumbersome design work of error estimation for specific time integration algorithms can be avoided. Regarding the numerical implementation, the local error estimation has a compact representation that it is determined by the time derivative variables at four successive time levels and only involves vector operations, which is simple for numerical implementation. Additionally, the adaptive time-stepping is further illustrated by the proposed error estimator and is used to solve the benchmark problems of lid-driven cavity and flow past a cylinder. Findings: The proposed computational procedure is capable of eliminating the nonphysical oscillations in GS4-1(1,1)/Crank–Nicolson method; being CPU-efficient in both dissipative and nondissipative schemes with better solution accuracy; and detecting the complex physics and hence selecting a suitable time step according to the user-defined error threshold. Originality/value: To the best of the authors' knowledge, for the first time, this study applies the general purpose GS4-1 family of time integration algorithms for transient simulations of incompressible Navier–Stokes equations in fluid dynamics with constant and adaptive time steps via a novel and universal error estimator. The proposed computational framework is simple for numerical implementation and the time step selection based on the proposed error estimation is efficient, benefiting to the computational expense for transient simulations. [ABSTRACT FROM AUTHOR]