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

TL;DR

This paper introduces an efficient, fully decoupled finite difference scheme for simulating wormhole propagation with heat transfer on staggered grids, emphasizing positivity preservation and optimal error estimates.

Contribution

It develops a novel linear, fully decoupled finite difference method with proven positivity and optimal error bounds for complex coupled systems involving heat and flow in porous media.

Findings

Numerical experiments confirm theoretical error estimates.

Method effectively handles 2D and 3D wormhole simulations.

Positivity preservation ensures physical reliability of simulations.

Abstract

In this paper, we construct an efficient linear and fully decoupled finite difference scheme for wormhole propagation with heat transmission process on staggered grids, which only requires solving a sequence of linear elliptic equations at each time step. We first derive the positivity preserving properties for the discrete porosity and its difference quotient in time, and then obtain optimal error estimates for the velocity, pressure, concentration, porosity and temperature in different norms rigorously and carefully by establishing several auxiliary lemmas for the highly coupled nonlinear system. Numerical experiments in two- and three-dimensional cases are provided to verify our theoretical results and illustrate the capabilities of the constructed method.