numerical aspects of wave propagations in a biot medium

FABIO IVÁN ZYSERMAN; JUAN E. SANTOS

MECANICA COMPUTACIONAL

AMCA

Lugar: Santa Fe; Año: 2006 vol. 25 p. 979 - 992

Biot's equations appear in geophysical applications where wave propagation in fluid 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 finite element solutions for propagating wavesdeteriorate 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 finite element method used to approximate the solution of the 1DBiot 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.