Numeric Simulation of wave propagation in diverse media using finite-difference approach

Abstract

The propagation of mechanical waves is a natural or artificial phenomenon and is transmitted in a medium; its propagation is modeled using partial differential equations, which must be solved numerically. The derivatives with respect to time and space are solved using a second-order approximation through centered finite difference operators. Because the modeling is carried out in depth, the values of the spatial axes are considered positive when depth increases. Also considering velocities and efforts within a stepped mesh, which takes into account the deformation generated in the medium due to the efforts and the impact of the wave in said medium. This deformation effect will be analyzed mathematically taking into account the Lamé coefficients, given that the medium through which the wave propagates is isotropic. Reflection and transmission of the wave will also be analyzed to look at its natural behavior. Since the wave modeling is computational, a treatment is made to the conditions of stability and numerical dispersion to avoid obtaining erroneous results and to be able to visualize the wave with a more realistic behavior. Edge absorption methods were analyzed to avoid the visualization of false reflections not existing in the elastic medium.