Numerical Algorithm for Unsteady Nonisothermal Two-Phase Flow in a Porous Cavity

In this paper, the problem of nonisothermal two-phase flow in a porous cavity has been investigated numerically. The conservation laws of energy, momentum, and mass are used to model the problem. The mixed Dirichlet-Neumann boundary conditions are used to describe the cavity boundaries. The equations system is converted into a dimensionless system in terms of Prandtl, Reynolds, Bond, capillary, and Darcy numbers. A time-splitting multiscale scheme has been developed to treat the time derivative discretization. Also, the Courant-Friedrichs-Lewy stability condition is utilized to adapt the time step size. Darcy’s law and continuity equation are coupled to compute the pressure, then, the energy equation is solved implicitly. The effects of Prandtl, Reynolds, Bond, capillary, and Darcy numbers on the pressure, velocity, temperature, saturation, and local Nusselt number have been investigated.