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[en] A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors

[en] In this paper the problem of the numerical approximation of the minimal global B-attractor M for a semiflow generated by the Navier-Stokes equations in a two-dimensional bounded domain Ω is considered. The method suggested here is based on the formula M = lim G^N, where G^N is a sequence of compact subsets of L₂ (Ω), N→∞ G^N contains M. The procedure of constructing G^N is finite and includes the numerical solution of the Navier-Stokes equations by means of the Galerkin method, together with an explicit finite-difference discretization in time

[en] We analyze a control problem for a phase field system modeling the solidification process of materials that allow two different types of crystallization coupled to a Navier–Stokes system and a nonlinear heat equation, with a reduced number of controls. We prove that this system is locally exactly controllable to suitable trajectories, with controls acting only on the motion and heat equations.

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[en] Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.

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[en] A renormalization group calculation of forced helical turbulence is presented. It is shown that: (i) helicity produces an additional term, which is an irrelevant perturbation of the viscous damping; (ii) the helical part of the forcing is never more than a marginal perturbation; (iii) when the magnetohydrodynamics equations are used instead of the Navier-Stokes equations, helicity generates a relevant perturbation of the Joule damping, proportional to curl b (b = magnetic field)

[en] The reduction of the truncation error including numerical diffusion, has been one of the most important tasks in the development of numericl methods. The stream line method is used to cancel cross numerical diffusion and some of the non-diffusion type truncation error. The two-step stream line method which is the combination of the stream line method and finite difference methods is developed in this work for the solution of the governing equations of incompressible buoyant turbulent flow. This method is compared with the finite difference method. The predictions of both classes of numerical methods are compared with experimental findings. Truncation error analysis also has been performed in order to the compare truncation error of the stream line method that of finite difference methods. (Author)