The numerical integration of the hydrodynamical model of semiconductors based on Extended Thermodynamics has been tackled. On account of the mathematical complexity of the system no theoretical conditions of convergence are available for the existing schemes. Therefore in order to lend conndence to the obtained numerical solution it was almost mandatory to resort to a cross-validation comparing...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

Non-oscillatory schemes are widely used in numerical approximations of nonlinear conservation laws. The Nessyahu-Tadmor (NT) scheme is an example of a second order scheme that is both robust and simple. In this paper, we prove a new stability property of the NT scheme based on the standard minmod reconstruction in the case of a scalar strictly convex conservation law. This property is similar t...

Central schemes may serve as universal finite-difference methods for solving nonlinear convection–diffusion equations in the sense that they are not tied to the specific eigenstructure of the problem, and hence can be implemented in a straightforward manner as black-box solvers for general conservation laws and related equations governing the spontaneous evolution of large gradient phenomena. T...

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W−1,∞ to the ’expected’ averages and obtain a sharp W−1,∞-convergence rate of order O(ε) – the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this weak...

Based on Nessyahu and Tadmor’s nonoscillatory central difference schemes for one-dimensional hyperbolic conservation laws [16], for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented. The experiments show the wide applicability of these multidimensional schemes. The theoretical arguments which support this are some m...

Bipolar semiconductor device 2D FDTD modelling suited to parallel computing is investigated in this paper. The performance of a second order explicit approximation, namely the Nessyahu-Tadmor scheme (NT2) associated with the decomposition domain method, are compared to a classical quasi-linear implicit one based on the Alternating Direction Implicit method (ADI). The comparison is performed bot...

Abstract. The nonoscillatory central difference scheme of Nessyahu and Tadmor is a Godunovtype scheme for one-dimensional hyperbolic conservation laws in which the resolution of Riemann problems at the cell interfaces is bypassed thanks to the use of the staggered Lax–Friedrichs scheme. Piecewise linear MUSCL-type (monotonic upstream-centered scheme for conservation laws) cell interpolants and ...

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations.A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two nonstandard formulations, that numerous F...