High-Order Bound-Preserving Finite Difference Methods for Incompressible Wormhole Propagation
High-Order Bound-Preserving Finite Difference Methods for Incompressible Wormhole Propagation
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DOI：
10.1007/s10915-021-01619-4
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发表时间：
2021-08
影响因子：
2.5
通讯作者：
Xinyuan Liu;Yang Yang-Yang;Hui Guo
中科院分区：
文献类型：
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作者：
Xinyuan Liu;Yang Yang-Yang;Hui Guo
在这篇文章中，我们继续我们在郭等人(J Comput Phys406：109219,2020年)中发展高阶保界(BP)有限差分(FD)方法的努力。我们将构造不可压缩虫洞传播的高阶BP FD格式。利用虫孔传播描述了碳酸盐岩储层在酸化过程中酸的孔道演化和孔隙度增加的现象。在虫洞传播中，酸浓度和孔隙率的重要物理性质涉及它们在0到1之间的边界和单调增加的孔隙率。高阶BP-FD方法可以在保持高阶精度的同时，保持这些重要的物理性质。其主要思想是在BP技术中选择合适的时间步长，在压力方程和浓度方程之间构造一致的流量对，从而推导出重影方程。因此，我们可以将正性保持技术应用于原始方程和推导出的方程。此外，参数化流量限制器还达到了高阶精度。数值实验验证了该格式的高阶精度和有效性。
In this paper we continue our effort in Guo et al. ( J Comput Phys 406:109219, 2020) for developing high-order bound-preserving (BP) finite difference (FD) methods. We will construct high-order BP FD schemes for the incompressible wormhole propagation. Wormhole propagation is used to describe the phenomenon of channel evolution of acid and the increase of porosity in carbonate reservoirs during the acidization of carbonate reservoirs. In wormhole propagation, the important physical properties of acid concentration and porosity involve their boundness between 0 and 1 and the monotonically increasing porosity. High-order BP FD methods can maintain the high-order accuracy and keep these important physical properties, simultaneously. The main idea is to choose a suitable time step size in the BP technique and construct a consistent flux pair between the pressure and concentration equations to deduce a ghost equation. Therefore, we can apply the positivity-preserving technique to the original and the deduced equations. Moreover, the high-order accuracy is attained by the parametrized flux limiter. Numerical experiments are presented to verify the high-order accuracy and effectiveness of the given scheme.