Wave propagation with irregular dissipation and applications to acoustic\n problems and shallow waters

2017/05/03 by Juan Carlos Muñoz, Michael Ruzhansky, Munoz, Juan Carlos +3 · 1 citation
Computer Science · Mathematics · Earth and Planetary Sciences · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Underwater Acoustics Research

paper · pdf · doi:10.48550/arxiv.1705.01401

Abstract

In this paper we consider an acoustic problem of wave propagation through a\ndiscontinuous medium. The problem is reduced to the dissipative wave equation\nwith distributional dissipation. We show that this problem has a so-called very\nweak solution, we analyse its properties and illustrate the theoretical results\nthrough some numerical simulations by approximating the solutions to the full\ndissipative model for a particular synthetic piecewise continuous medium. In\nparticular, we discover numerically a very interesting phenomenon of the\nappearance of a new wave at the singular point. For the acoustic problem this\ncan be interpreted as an echo effect at the discontinuity interface of the\nmedium.\n

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