An Inexact Newton Method for Fully Coupled Solution of the Navier–Stokes Equations with Heat and Mass Transport

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

doi:10.1006/jcph.1997.5798

Cited by 66 publications

(76 citation statements)

References 12 publications

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“…A Newton-Krylov method [22] is an implementation of Newton's method in which a Krylov iterative solution technique is used to approximately solve the linear systems that are generated at each step of Newton's method. Specifically, to solve the nonlinear system , the Krylov iterative solver is applied to determine an approximate solution of…”

Section: Newton-krylov Methodsmentioning

confidence: 99%

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Salinger

Lehoucq

Pawlowski

et al. 2002

Numerical Methods in Fluids

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Summary:Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability analysis are used to study transition from steady to transient flow as a function of Rayleigh number. To carry out this study the steady state form of the governing PDEs is discretized using a Galerkin/Least Squares Finite Element formulation, and solved on parallel computers using a fully coupled Newton method and preconditioned Krylov iterative linear solvers. Linear stability analysis employing a large scale eigenvalue capability is used to determine the stability of the steady solutions. The boundary between steady and time dependent flows is determined by a Hopf bifurcation tracking capability that is used to directly track the instability with respect to the aspect ratio of the system and with respect to mesh resolution. The effect of upwinding stabilization terms in the finite element formulation on the computed value of critical Rayleigh number is investigated. The Hopf bifurcation signaling the onset of flow is determined to occur at a critical Rayleigh number of .

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Section: Newton-krylov Methodsmentioning

confidence: 99%

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Salinger

Lehoucq

Pawlowski

et al. 2002

Numerical Methods in Fluids

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“…In our earlier study [15], we implemented a Newton-GMRES method with a backtracking globalization in the parallel finite-element reacting flow code MPSalsa [13]. Briefly, MPSalsa uses a Galerkin least-squares (GLS) formulation for the spatial discretization, an [14]).…”

Section: An Illustrative Experimentsmentioning

confidence: 99%

“…Also, no fixed value of is likely to be suitable for a broad range of problems. Adaptive choices that incorporate information about F have been shown to be most widely effective in the numerical experiments in [15]. Indeed, in the experiments in [15], the problem discussed here was successfully solved using such choices.…”

Section: An Illustrative Experimentsmentioning

confidence: 99%

“…It was demonstrated in [15], as well as in previous experiments in [7] and [11], that requiring too much accuracy in solving the linear subproblems can cause Newton-GMRES methods to become less robust, even with a backtracking globalization. In particular, it was shown that requiring too much accuracy may result in more frequent failure of the backtracking routine to determine an acceptable step, as well as inefficiency.…”

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confidence: 94%

“…Newton-GMRES methods are representative of the broader class of Newton-Krylov methods and have enjoyed considerable success in fluid flow applications. Following [15], we assume the primary mechanism for enhancing robustness is a backtracking (linesearch, damping) technique that shortens steps as necessary to ensure adequate decrease in the residual of the nonlinear system. 5 (See [7], [11], and [15] for discussions of the implementation of backtracking in Newton-GMRES methods and experiments that show its effectiveness on fluid flow applications and other large-scale problems; see also [5] for a general treatment of backtracking for exact Newton's method and [6] for a discussion of backtracking for general inexact Newton methods.…”

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confidence: 99%

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On Backtracking Failure in Newton–GMRES Methods with a Demonstration for the Navier–Stokes Equations

Tuminaro

Walker

Shadid

2002

Journal of Computational Physics

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In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the NavierStokes equations with heat and mass transport. Specifically, it was observed that a Newton-GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier-Stokes equations. c 2002 Elsevier Science (USA)

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Mathematical Preliminaries

2020

Control in Bioprocessing

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An Inexact Newton Method for Fully Coupled Solution of the Navier–Stokes Equations with Heat and Mass Transport

Cited by 66 publications

References 12 publications

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

On Backtracking Failure in Newton–GMRES Methods with a Demonstration for the Navier–Stokes Equations

Mathematical Preliminaries

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