Structure-preserving algorithm for thermal conduction of local thermal nonequilibrium saturated porous medium

Abstract

Based on the two-energy equation model and constitutive equations of local thermal nonequilibrium saturated porous media, one-dimensional thermal conduction equations of solid skeleton and pore fluid are established. Introducing orthogonal variables, a first order generalized multi-symplectic structure-preserving form of thermal conduction equations is derived as well as the errors of generalized multi-symplectic conservation law and local momentum. The temperature profiles of two phases are obtained and the effect of the heat exchange coefficient between two phases on the process from local thermal nonequilibrium to local thermal equilibrium is revealed numerically. According to the relative error between numerical solution and analytical solution derived from the separating variables method, it can be concluded that this structure-preserving scheme is a valid scheme with high accuracy. Numerical errors of generalized multi-symplectic conservation law and local momentum are presented for two typical types of the thermal conduction in one-dimensional saturated porous media. According to these numerical results, it can be concluded that this structure-preserving algorithm has long-time numerical stability and good conservation properties.