High-Order Bound-Preserving Finite Difference Methods for Incompressible Wormhole Propagation

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.