A Newton-Krylov Algorithm with a Loosely-Coupled Turbulence Model for Aerodynamic Flows

Blanco, Max; Zingg, David W.

doi:10.2514/6.2006-691

Cited by 7 publications

(6 citation statements)

References 18 publications

(32 reference statements)

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“…Despite the fact that no attempt to hand tune the parameters of the globalization strategy was made, the run time in terms of equivalent residual evaluations is competitive with that reported elsewhere. In particular, Blanco and Zingg report [33] that the Newton-Krylov algorithm applied to a second-order accurate matrix-dissipation scheme required the equivalent of 660 residual evaluation to converge for the same transonic case. However due to the differences in the discretization scheme and the mesh used, too much emphasis should not be placed on such direct comparisons.…”

Section: Overall Memory and Computational Costmentioning

confidence: 98%

Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

Michalak¹,

Ollivier‐Gooch²

2010

Computers & Fluids

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Section: Overall Memory and Computational Costmentioning

confidence: 98%

Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

Michalak¹,

Ollivier‐Gooch²

2010

Computers & Fluids

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“…8 When an iterative solver, such as Newton's method, is implemented, decoupling the system allows the computational efficiency to be increased as it means that two smaller systems are solved. Decoupling the two systems also allows a different turbulence model to be implemented with greater ease.…”

Section: Model Decouplingmentioning

confidence: 99%

Improved Efficiency for the Numerical Continuation of RANS Equations

Huntley

Jones

Gaitonde

2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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The numerical continuation of the Reynolds Averaged Navier-Stokes equations involves computation of the solution of large non-linear systems, resulting in high computational cost. Three different methods are implemented to reduce the computational cost of these calculations. Firstly, the turbulence model is decoupled from the main flow equations allowing two smaller systems to be solved. The Recursive Projection Method is implemented to allow existing time integration techniques to be used in the computation of unstable solutions. Finally, bifurcation tracking methods are presented that allow the bifurcation point to be tracked with two parameters without the need for multiple continuation runs. The decoupling method works up to parameter values close to the bifurcation point, where flow separation occurs and the cross-derivative terms in the Jacobian become more important. The Recursive Projection Method shows potential in extending the applicability of time integration methods by allowing them to converge onto unstable solutions. The bifurcation trackers successfully follow the Hopf bifurcation in multiple parameters allowing loci of bifurcations to be mapped in two parameter space. Results are shown for aerofoils at a range of transonic conditions.

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“…Their efficiency in the context of a Newton-Krylov method was shown in [6,36]. Efficiency of block level-based preconditioners is illustrated in [22].…”

Section: Introductionmentioning

confidence: 98%

The importance of structure in incomplete factorization preconditioners

Scott

Tůma

2010

Bit Numer Math

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In this paper, we consider level-based preconditioning, which is one of the basic approaches to incomplete factorization preconditioning of iterative methods. It is well-known that while structure-based preconditioners can be very useful, excessive memory demands can limit their usefulness. Here we present an improved strategy that considers the individual entries of the system matrix and restricts small entries to contributing to fewer levels of fill than the largest entries. Using symmetric positive-definite problems arising from a wide range of practical applications, we show that the use of variable levels of fill can yield incomplete Cholesky factorization preconditioners that are more efficient than those resulting from the standard level-based approach. The concept of level-based preconditioning, which is based on the structural properties of the system matrix, is then transferred to the numerical incomplete decomposition. In particular, the structure of the incomplete factorization determined in the symbolic factorization phase is explicitly used in the numerical factorization phase. Further numerical results demonstrate that our level-based approach can lead to much sparser but efficient incomplete factorization preconditioners.

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A Newton-Krylov Algorithm with a Loosely-Coupled Turbulence Model for Aerodynamic Flows

Cited by 7 publications

References 18 publications

Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

Improved Efficiency for the Numerical Continuation of RANS Equations

The importance of structure in incomplete factorization preconditioners

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