Numerical Aspects Of Wave Propagation In A Biot Medium

Abstract

Biot's equations appear in geophysical applications where wave propagation in _uid saturated
porous media is considered, although in recent years they have also been applied to model ultrasonic
technics for osteoporosis or other bone-modifying diseases diagnosis.
It is well known that _nite element solutions for propagating waves deteriorate rapidly with increasing
dimensionless wavenumber, even when the number of elements per wavelength is kept constant; this is
referred to as pollution error.
In this work we present a detailed analysis of the numerical behaviour of a _nite element method used to
approximate the solution of the 1D Biot equations.
The study is performed by deriving and the dispersion relations and by evaluating the derived quantities,
such as the dimensionless phase and group velocities.