A classi cation in terms of accuracy of ux limited high resolution schemes in steep gradient region is done based on two di erent total variation (TV) stability region. The dependence of TV stability region on the smoothness parameter is discussed which relates these two TV stability regions. A common unifying TV stability region is proposed for both class of schemes. Moreover new ux limiters, ...

In this paper a new type electrical devices, designed for use in medium voltage and high voltage grids, has been explained – the fault current limiters. Their principals of operation and different structures have been proposed. The comparative analysis and their possibile estimation have been made.

We propose a strategy to perform second-order enhancement using slope-limiters for the simultaneous linear advection of several scalar variables. Our strategy ensures a discrete min-max principle not only for each variable but also for any number of non-trivial combinations of them, which represent control variables. This problem arises in fluid mechanics codes using the Arbitrary Lagrange-Eule...

A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods’ main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, ...

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the m...