Current Issue : April-June Volume : 2023 Issue Number : 2 Articles : 5 Articles
In this paper, we propose a fully decoupled and linear scheme for the magnetohydrodynamic (MHD) equation with the backward differential formulation (BDF) and finite element method (FEM). To solve the system, we adopt a technique based on the “zero-energy-contribution” contribution, which separates the magnetic and fluid fields from the coupled system. Additionally, making use of the pressure projection methods, the pressure variable appears explicitly in the velocity field equation, and would be computed in the form of a Poisson equation. Therefore, the total system is divided into several smaller sub-systems that could be simulated at a significantly low cost. We prove the unconditional energy stability, unique solvability and optimal error estimates for the proposed scheme, and present numerical results to verify the accuracy, efficiency and stability of the scheme....
The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively; and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010)....
Let us consider higher dimensional canards in a sow-fast system R22 with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a key notion “symmetry” to the slow-fast system, it becomes clear when the pseudo singular point obtains the structural stability or not. It should be treated with a general case. Then, it will also be given about the sufficient conditions for the existence of the center manifold under being “symmetry”. The higher dimensional canards in the sow-fast system are deeply related to Hilbert’s 16th problem. Furthermore, computer simulations are done for the systems having Brownian motions. As a result, the rigidity for the system is confirmed....
The ongoing study has been vehemently allocated to propound an ameliorated α-weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using α-weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved....
In this study, two-phase non-Newtonian turbulent fluid flow in an inclined geothermal pipe with chemical reaction was considered. The governing nonlinear partial differential equations derived were solved numerically using Finite Difference Method. Influence of flow parameters on the temperature, concentration and velocity profiles were analyzed graphically. From the mathematical analysis of the model, it was established that the chemical reaction parameter significantly influenced the concentration distribution in both gaseous and liquid phases. Findings further revealed that decreasing the chemical reaction parameter resulted in decreased concentration of the geothermal fluid, which causes corrosion of geothermal pipes. These findings provide important information to engineers and researchers in making better decisions in terms of design, sizing and maintenance of flow systems in geothermal pipes....
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