Numerical analysis of some typical Finite Differences simulations of the waves propagation through different media

Abstract

The Numerical Physics field has its specific phenomena, which intervene always but are confined usually to very restricted limits. However, the description possibilities (accuracy, computing time, etc) of computers are limited and sometimes - in strong connection with some specific features of the used algorithms and the computer errors - the numerical phenomena reach important amplitudes, the accomplished numerical simulations presenting significant distortions relative to the simulated (true) physical evolutions. That is why the goal of this work is to study the main features of some classical and newly found out numerical phenomena associated to the Finite Differences (FD) simulations of the wave propagation through media with sharp interfaces and attenuative character (considered as suddenly-emerging phenomena), and of other physical processes. The mechanisms of these numerical phenomena were studied in detail, the obtained findings allowing us to predict the distortions of the simulated physical processes. Of course, the good knowledge of the main features and of the mechanisms of the most important numerical phenomena allows us also to avoid the appearance of drastic distortions of the simulated evolutions, as well as the optimization of some numerical simulations. © Springer-Verlag Berlin Heidelberg 2005.