中文摘要：

首次将高精度时空守恒元/解元方法推广到可压缩流体饱和孔隙介质中孔隙压力波传播的数值计算中。将孔隙度梯度从源（汇）项中分离，直接引入流通量，改进了理论模型。通过对孔隙介质激波问题的数值模拟，验证了方法的精度和有效性。在此基础上，提出了孔隙介质中二维黎曼问题，并揭示了孔隙压力波存在接触间断、激波、膨胀波、压缩波等复杂的结构特征。该成果对二氧化碳地质封存、二氧化碳提高石油采收率、页岩气压裂开采以及地震破裂过程的研究具有重要的理论与应用意义。

英文摘要：

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.