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.

在本文中，我们继续在郭等人的努力。( J Comput Phys 406:109219, 2020) 用于开发高阶保界 (BP) 有限差分 (FD) 方法。我们将为不可压缩的虫洞传播构建高阶 BP FD 方案。虫洞传播用于描述碳酸盐岩储层酸化过程中酸的通道演化和碳酸盐岩储层孔隙度增加的现象。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 和 1 之间的界限以及单调增加的孔隙率。高阶 BP FD 方法可以保持高阶精度并同时保持这些重要的物理特性。主要思想是在 BP 技术中选择合适的时间步长，并在压力和浓度方程之间构建一致的通量对以推导出鬼方程。因此，我们可以对原始方程和推导方程应用保正性技术。此外，高阶精度是通过参数化磁通限制器实现的。数值实验被提出来验证给定方案的高阶精度和有效性。