A mass-lumped mixed finite element method for acoustic wave propagation

A mixed finite element approach for viscoelastic wave propagation

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zener’s model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass l...

A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description.

A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian-Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties...

An analysis of mixed finite element approximations for periodic acoustic wave propagation

Wave propagation across acoustic / Biot’s media: a finite-difference method

Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect...

Finite Element Heterogeneous Multiscale Method for Transient Wave Propagation

A finite element heterogeneous multiscale method (FEHMM) is proposed for the time dependent wave equation with highly oscillatory, albeit not necessarily periodic, coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coefficients are computed “on the fly” on sampling domains within each macro finite eleme...