Preliminary verification of incompressible Navier-Stokes equations solved by The Newton method

Abstract

The thermal-hydraulics module for reactor multi-physics coupling is studied. Multi-physics coupling for high temperature gas cooling reactor is very important due to the interaction between different physics, especially neutronics and thermal-hydraulics. This paper demonstrates an Incompressible Navier-Stokes (INS) module in the Multiphysics Object-Oriented Simulation Environment (MOOSE) to validate the accuracy and efficiency of the module, and the research on INS module is the significant basis of the future coupling work. MOOSE is an open-source finite element platform developed by Idaho National Lab (INL), which is for solving nonlinear equations from different physics simultaneously and can also couple different codes implicitly. The Jacobian-free Newton Krylov (JFNK) method adopted in MOOSE uses the finite difference method to avoid explicitly solving the Jacobian matrix so as to effectively save memory, and different preconditioning methods are also applied to accelerate the Krylov iteration. Besides, the Newton method is also supplied in MOOSE to solve nonlinear equations. Incompressible Navier-Stokes equations have been solved by the Newton method through the finite element method in MOOSE, and different numerical solution methods can be used to solve different cases. MOOSE regards problem equations as kernels and boundary conditions, and solves the discretized equations using the embedded Petsc or Trilinos solver. A convective heat transfer lid driven cavity problem is calculated using the INS module and the CFD tool Fluent to compare simulation results, and the temperature average error of 0.31% validates the module accuracy. In addition, JFNK and Newton methods are adopted to solve the same problem, and the results reveal that Newton method can save nearly 23% of the calculation time and has higher efficiency. The simulation results prove the module capability of applying to the reactor thermal-hydraulics, multi-physics coupling and safety analysis.