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We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with
large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to
a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface
between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many
small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles,
slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method
for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry,
as long as it aligns with the grid. We prove optimal global first-order L
2 convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify
these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower
dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface
in transition to the Stokes elements. 相似文献
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With the study of faunal remains (zooarchaeology) emerging as an increasingly prominent component of archaeological studies in China, the importance of studying processes of assemblage formation and preservation (taphonomy) is becoming evident. Remains of animals recovered from an archaeological site are a biased sample of the assemblage that was originally deposited because certain animal parts preserve better than others. Important characteristics of faunal assemblages, such as skeletal element representation and age profiles, can be affected by differential preservation caused by taphonomic agents, both cultural or natural. One primary goal of taphonomic studies is to provide an understanding of differential preservation of bone elements, allowing archaeologists to make more accurate assessments concerning the exploitation of different animal species by past peoples. Recent studies of the faunal assemblages from the Early Paleolithic site of Xujiayao and the Neolithic site of Taosi, both in Shanxi Province, provide examples of the effects that differential preservation can have on archaeological interpretations of skeletal element representation and age profiles, respectively. These examples illustrate how an understanding of taphonomy is critical to the future practice of zooarchaeology in China. 相似文献
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The vaterite form of calcium carbonate seldom occurs in geological formations or during chemical processing. However, vaterite crystals form during the liquefaction of a Wyoming subbituminous coal. Gravitational separation of the coal showed vaterite to form because of the presence of some other mineral in the coal matrix. Model compound studies with calcium acetate identified silica and possibly iron pyrite to be minerals found in coal which seed vaterite crystals. 相似文献
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