Numerical investigation of an incompressible multiphase flow with heat conduction and iterative solution of the discretized transport equations

A system of equations for a nonsteady, incompressible, laminar multiphase flow, coupled with heat conduction, is considered, where the unknowns are the velocities, pressures, and temperatures of the phases. An implicit difference scheme is proposed and theoretically investigated. Convergence in the L2 norm is proved for the velocities and temperatures, and stability of the solutions is established. An iterative solution is justified which is especially suitable for low Reynolds numbers and small viscosity fluctuations. Implicit difference equations are used to improve the convergence rate.