In this paper, a 2D numerical modeling of sound wave propagation in a shallow water medium that acts as a waveguide, are presented. This modeling is based on the method of characteristic which is not constrained by the Courant–Friedrichs–Lewy (CFL) condition. Using this method, the Euler time-dependent equations have been solved under adiabatic conditions inside of a shallow water waveguide which is consists of one homogeneous environment of water over a rigid bed. In this work, the stability and precision of the method of characteristics (MOC) technique for sound wave propagation in a waveguide were illustrated when it was applied with the semi-Lagrange method. The results show a significant advantage of the method of characteristics over the finite difference time domain (FDTD) method.

The ILC is an immense e+e- machine planned since 2004 by a large international collaboration, to be potentially built in Japan [1]. The gigantic size of the whole research infrastructure, the involved human, technical and financial resources, and the pressure of new emerging and potentially soon to be competitive accelerator technologies, make the final building decision quite difficult. A vivid debate is carried on this subject globally by involved accelerator research communities. The European voice is very strong and important in this debate, and has recently been essentially refreshed by clear statements in a few official documents [2]. The final HEP European Strategy Document is just under preparation. This paper is a very modest and subjective voice in this debate originating from Poland, which around 50 researchers are present at the list of 2400 signatories for the original ILC TDR document published in 2013 [3].