High-order numerical simulation of axisymmetric wave phase conjugation

Abstract

In the present paper, a general physico-mathematical model of magneto-acoustic Wave Phase Conjugation (WPC) is proposed, which includes wave propagation both in solid zones (the conjugator itself and other solid regions, if present) and in fluid zones surrounding the conjugator. Acoustic waves in the solid zones are assumed to behave linearly while in the fluid zones the waves may be either linear or non-linear. The axisymmetric governing equations of the model are discretized on an unstructured triangular mesh with a modified version of the Nodal Discontinuous Galerkin (NDG) method, which is a compact, high-order technique based on non-collocated solution and flux bases. The third-order Strong Stability-Preserving (SSP) Runge-Kutta (RK) scheme is used for integration in time. To avoid any false reflections from the outer boundaries of the computational domain the Nearly Perfectly Matched Layer (NPML) technique is adopted. A comprehensive set of test problems addressing all facets of the proposed numerical model is used for verification via comparison with analytical solutions. After the accuracy, performance, and reliability of the proposed model are established, two WPC problems are numerically simulated for the linear and weakly non-linear regimes. The main WPC properties, such as retro-focusing and parametric resonance, are observed in the numerical experiments with good accuracy.