An Inexact Newton Method for Fully-Coupled Solution of the Navier-Stokes Equations with Heat and Mass Transport; SAND97-0132
Albuquerque, NM: Sandia National Laboratories, 1997. Presumed First Edition, First printing. Tape bound. 28, [8] pages, plus covers. Formulae. Footnotes. Figures. Tables. Sandia computational scientist John N. Shadid was awarded the Thomas J.R. Hughes Medal from the United States Association for Computational Mechanics in 2019. The medal is given “in recognition of outstanding and sustained contributions to the broad field of Computational Fluid Dynamics that significantly advance the understanding of theories and methods impacting CFD.” John, with a master’s degree in mathematics and a doctorate in mechanical engineering from the University of Minnesota, won “for outstanding and sustained contributions to large-scale parallel multiphysics computational-fluid-dynamics solution methods, high-performance computing algorithms/software and numerical methods for coupled nonlinear partial differential equations.” Workers in the field have modelled fast phenomena such as the hypervelocity impact of solids and the propagation of shocks and waves in inertial confinement fusion systems. Raymond S. Tuminaro is with the Center for Computer Research at Sandia and he is interested in parallel iterative methods for linear systems, numerical linear algebra, eigenvalue problems, and parallel numerical software. Special interests in algebraic multigrid, numerical solution of Maxwell's equations, incompressible Navier-Stokes, and block preconditioning. He developed the Aztec iterative library as well as the ML multilevel preconditioning package. I was also part of the MueLu development team. Homer F. Walker, Professor Emeritus Mathematical Sciences Department Worcester Polytechnic Institute. This work was later published in JOURNAL OF COMPUTATIONAL PHYSICS 137, 155–185 (1997) ARTICLE NO. CP975798.
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 PetrovGalerkin 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. Condition: Very good.
Keywords: Navier–Stokes equations; inexact Newton methods; Newton iterative (truncated Newton) methods; Newton–Krylov methods
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