  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.
