Using K-Branch Entropy Solutions for Multivalued Geometric Optics Computations

This paper is devoted to a numerical simulation of the classical WKB system arising in geometric optics expansions. It contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous. We address the problem of treating it in such a way that superimposed signals can be reproduced by means of the kinetic formulation of “multibranch solutions,” originally due to Brenier and Corrias. Some existence and uniqueness results are given, together with computational test cases of increasing difficulty displaying up to five multivaluations.