Analysis of the Numerical Dispersion of Waves in Saturated Poroelastic media

FABIO I. ZYSERMAN; JUAN E. SANTOS

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Elsevier

Año: 2007 vol. 196 p. 4644 - 4655

0045-7825

This work presents the  analysis of the numerical dispersion propertiesof a finite element method used to approximate the solution ofthe equations ofmotion for a fluid saturated porous elastic solid (a Biot medium) inthe twodimensional case and  the low frequency regime.The finite element method employed comprises a nonconforming rectangularelement for the approximation of each component of the  displacement vectorin the solid phase, and the Raviart-Thomas-Nedelecmixed finite element space of zero order for the fluid phase. The study is carried out by constructing and analyzing analytic and numericaldimensionless dispersion relations, and by evaluatingderived quantities such as dimensionless phase and group velocities anddimensionless attenuation for the three type of waves predicted by Biot´sequations of motion as a measure of the numerical distortion.It is observed that the finite element procedure introduces bothnumerical dispersion and anisotropy in all three waves in a similarfashion; however, only the slow wave displayed a significantfrequency dependent behaviour. It was also observed that the loss of accuracyis more important for the dimensionless attenuationthan for the dimensionless group or  phase velocities.The analysis presented yieldslower bounds for the number of points per wavelength neededto reach a desired accuracy in the dimensionlessphase and group velocities and attenuation coefficients in Biot media.