An inexact Newton method for fully-coupled solution of the Navier--Stokes equations with heat and mass transport

John N. Shadid, Raymond S. Tuminaro, Homer F. Walker

Sandia National Laboratories
Albuquerque, New Mexico 87185


The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript we focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context we use a particular spatial discretization based on a pressure stabilized Petrov--Galerkin finite element formulation of the low Mach number Navier--Stokes equations with heat and mass transport. Our discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.