In the recent papers [4, 5] the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was formally motivated in these papers as a limiting case of an alignment term proposed by Motsch and Tadmor [6]. In this paper, we rigorously justify this ...

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional...

We design efficient numerical schemes for approximating the MHD equations in multidimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multidimensional (GMD) framework of [S. Mishra and E. Tadmor, Commun. Comput. Phys. 9 (2010) 688–710; S. Mishra and E. Tadmor, SIAM...

Here, we indicate how to integrate the set of conservation equations for mass, momentum and energy for a two-fluid plasma coupled to Maxwell’s equations for the electromagnetic field, written in a composite conservative form, by means of a recently modified non-staggered version of the staggered second order central difference scheme of Nessyahu and Tadmor [H. Nessyahu, E. Tadmor, Non-oscillato...

In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W 1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert weak pointwise-error estimates to optimal...

We discuss the concentration factor methods for determination of jumps in terms of spectral data. The results are relative to the classical Lukács Theorem and some recent results obtained by A. Gelb, E. Tadmor and F. Móricz. §

We improve the recent result of Chae and Tadmor (2008) [10] proving a one-sided threshold condition which leads to a finite-time breakdown of the Euler–Poisson equations in arbitrary dimension n. © 2009 Elsevier B.V. All rights reserved.

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax-Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented b...

Nonoscillatory central schemes are a class of Godunov-type (i.e., shock-capturing, finite volume) numerical methods for solving hyperbolic systems of conservation laws (e.g., the Euler equations of gas dynamics). Throughout the last decade, central (Godunov-type) schemes have gained popularity due to their simplicity and efficiency. In particular, the latter do not require the solution of a Rie...