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.

翻译：本文构造了一种交错网格上含热传输过程的虫洞传播高效线性全解耦有限差分格式，该格式在每个时间步仅需求解一系列线性椭圆方程。我们首先证明了离散孔隙度及其时间差商的正性保持性质，随后通过建立一系列辅助引理，对高度耦合的非线性系统精细地推导了速度、压力、浓度、孔隙度和温度在不同范数下的最优误差估计。二维和三维数值实验验证了理论结果，并展示了所构造方法的计算能力。