Explicit–implicit schemes for non-isothermal filtration problem: Single-temperature model

Abstract

In this paper, we consider a non-isothermal filtration model for a two-phase immiscible incompressible fluid, for the numerical implementation of which an explicit–implicit algorithm is proposed. The problem is presented in a mixed generalized formulation, and an explicit–implicit method of the IMPES type is used to calculate the pressure, full velocity and water saturation, and an explicit–implicit scheme is built to calculate the temperature and heat flux with explicit consideration of convective heat transfer. At the beginning of the article, the mechanism of temperature homogenization of according to temperature heterogeneous system is considered. In computational experiments, special attention is paid to the comparison of the non-isothermal model with the isothermal one, including the discussion of fingering instability.