Numerical modeling of transient two-dimensional viscoelastic waves

TL;DR

This paper presents an efficient numerical method for simulating transient two-dimensional viscoelastic waves using a first-order PDE system, memory variables, and advanced discretization techniques, enabling accurate modeling of complex wave phenomena.

Contribution

It introduces a novel numerical approach combining memory variables and splitting methods to accurately model viscoelastic wave propagation without convolutions.

Findings

Effective modeling of wave dissipation in viscoelastic media

Accurate simulation of multiple scattering configurations

Use of high-order ADER scheme for propagative part

Abstract

This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.