The governing equations of the propagation of shock waves in compressible fluid saturated deformable porous media are improved by the way the porosity gradient terms are treated in the flow flux vector. An updated space-time conservation element and solution element (CE/SE) method

which is a new approach in computational fluid dynamics (CFD)

is presented to depict global and local flux conservation in space-time domain. The physical model and the CE/SE method are both validated with the experimental study based on the head-on collision of a planar shock wave through a rigid porous material; and then good agreements are found to be evident. After that

the two-dimensional Riemann problem in the porous media is established. It is found that the wave structures of the pore pressure consist of shock waves

compaction waves

expansion waves and the contact discontinuity. To our best knowledge

this is the first time that pore pressure waves have been successfully simulated with the CE/SE method inside a multiphase deformable porous medium. The findings are potentially applicable to CO2 geological storage

CO2 enhanced oil recovery

shale gas exploration and earthquake rupture processes.