A three-dimensional code for the simulation of streamers is introduced. The code is based on a fluid model for oxygen-nitrogen mixtures that includes drift, diffusion and attachement of electrons and creation of new charge carriers through impact ionization and photo-ionization. The electric field created by the space charges is solved self-consistently. The code assumes that the streamer geome...

Problem statement: Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a...

It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a novel type of static kink solution which may occupy any position relative to the spatial lattice and experiences no Peierls-Nabarro barrier. Consequently the d...

The elastic wave equation in spherical coordinates is solved on a spherical section by a Chebyshev spectral method. In the presented algorithm the singularities in the governing equations are avoided by centering the physical domain around the equator. The highly accurate pseudo-spectral (PS) derivative operators reduce the required grid size compared to nite-diierence (FD) algorithms. The non-...

The simulation of ultrasound wave propagation through biological tissue has a wide range of practical applications. However, large grid sizes are generally needed to capture the phenomena of interest. Here, a novel approach to reduce the computational complexity is presented. The model uses an accelerated k-space pseudospectral method which enables more than one hundred GPUs to be exploited to ...

An experimental and numerical study is presented to investigate the breaking criterion of Song and Banner [J. Phys. Oceanogr. 32, 2541 (2002)] who suggested a threshold range of 3 (1.4 0.1) 10 for a predictive wave breaking parameter, measuring the rate of change of the local energy maximum and the local wave number, to differentiate between wave trains that lead to breaking and those that do n...

This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, ...

Spectral and pseudo spectral methods for advection equations are investigated. A basic framework is given which allows the application of techniques used in finite element analysis to spectral methods with trigonometric polynomials. Error estimates for semidiscrete spectral and pseudo spectral as well as fully discrete explicit pseudo spectral methods are given. The approximation schemes are sh...

We present a numerical method for studying the normal modes of accretion flows around black holes. In this first paper, we focus on two-dimensional, viscous, hydrodynamic disks in pseudo-Newtonian potentials, for which the linear modes have been calculated analytically in previous investigations. We use a pseudo-spectral algorithm to evolve the hydrodynamic equations and devise a number of test...