We present a novel numerical approach for the comprehensive, flexible,
and accurate simulation of poro-elastic wave propagation in cylindrical
coordinates. An important application of this method is the modeling
of complex seismic wave phenomena in fluid-filled boreholes, which
represents a major, and as of yet largely unresolved, computational
problem in exploration geophysics. In view of this, we consider a
numerical mesh consisting of three concentric domains representing
the borehole fluid in the center, the borehole casing and the surrounding
porous formation. The spatial discretization is based on a Chebyshev
expansion in the radial direction, Fourier expansions in the other
directions, and a Runge-Kutta integration scheme for the time evolution.
A domain decomposition method based on the method of characteristics
is used to match the boundary conditions at the fluid/porous-solid
and porous-solid/porous-solid interfaces. The viability and accuracy
of the proposed method has been tested and verified in 2D polar coordinates
through comparisons with analytical solutions as well as with the
results obtained with a corresponding, previously published, and
independently benchmarked solution for 2D Cartesian coordinates.
The proposed numerical solution also satisfies the reciprocity theorem,
which indicates that the inherent singularity associated with the
origin of the polar coordinate system is handled adequately.