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In this paper, we construct an efficient linear and fully decoupled finitedifference scheme for wormhole propagation with heat transmission process onstaggered grids, which only requires solving a sequence of linear ellipticequations at each time step. We first derive the positivity preservingproperties for the discrete porosity and its difference quotient in time, andthen obtain optimal error estimates for the velocity, pressure, concentration,porosity and temperature in different norms rigorously and carefully byestablishing several auxiliary lemmas for the highly coupled nonlinear system.Numerical experiments in two- and three-dimensional cases are provided toverify our theoretical results and illustrate the capabilities of theconstructed method.

On efficient linear and fully decoupled finite difference method for wormhole propagation with heat transmission process on staggered grids