A nearly-implicit hydrodynamic numerical scheme for two-phase flows
Journal of Computational Physics
Matrix-free methods for stiff systems of ODE's
SIAM Journal on Numerical Analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A discrete particle model for bubble-slug two-phase flows
Journal of Computational Physics
An approximate linearized Riemann solver for a two-fluid model
Journal of Computational Physics
Modelling of two-phase flow with second-order accurate scheme
Journal of Computational Physics
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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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.