Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction

This paper presents the solution of the two-phase flow equations coupled to nonlinear heat conduction using the Jacobian-free Newton–Krylov (JFNK) method which employs a physics-based preconditioner. Computer simulations will demonstrate that the implicitly balanced solution obtained from the JFNK method is more accurate than traditional approaches that employ operator splitting and linearizing. Results will also indicate that by employing a physics-based preconditioner the implicitly balanced solution can provide a more accurate solution for the same amount of computer time compared to the traditional approach for solving these equations. Finally, convergence plots will show that as the transient time lengthens, the implicitly balanced solution can maintain this higher level of accuracy at much larger time steps.