An Inexact Newton Method for Fully Coupled Solution of the Navier-Stokes Equations with Heat and Mass Transport
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TLDR
In this article, a nonlinear solution method based on an inexact Newton method with backtracking is proposed for the low Mach number Navier?Stokes equations with heat and mass transport.About:
This article is published in Journal of Computational Physics.The article was published on 1997-10-01 and is currently open access. It has received 90 citations till now. The article focuses on the topics: Navier–Stokes equations & Discretization.read more
Citations
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Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Dana A. Knoll,David E. Keyes +1 more
TL;DR: The aim of this paper is to present the reader with a perspective on how JFNK may be applicable to applications of interest and to provide sources of further practical information.
Journal ArticleDOI
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
TL;DR: This study considers the temporal-accuracy issue by presenting detailed numerical-convergence studies for problems related to radiation-diffusion simulations by considering time-integration methods that include fully implicit, semi-implicit, and operator-splitting techniques.
Journal ArticleDOI
Globalization Techniques for Newton-Krylov Methods and Applications to the Fully Coupled Solution of the Navier-Stokes Equations
TL;DR: This paper reviews several representative globalizations of Newton-Krylov methods, discusses their properties, and reports on a numerical study aimed at evaluating their relative merits on large-scale two- and three-dimensional problems involving the steady-state Navier-Stokes equations.
Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
TL;DR: In this paper, the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD was explored.
Journal ArticleDOI
Large‐scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers
TL;DR: In this paper, the eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem.
References
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GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Journal ArticleDOI
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
U Ghia,K.N Ghia,C. T. Shin +2 more
TL;DR: The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions.
Journal ArticleDOI
An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.